Factors of 210

Factors of 210

Factors of a number refer to the numbers that divide the given number without leaving a remainder. In this blog, we will explore the factors of 210 and understand their properties.

Answer to Factors of 210

The factors of 210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

How to solve the problem: hints

To find the factors of 210, follow these steps:

1. Determine the criteria for judging whether a number is a factor. A number is a factor of 210 if it divides 210 without leaving a remainder.

2. List all the numbers starting from 1 up to the given number, which is 210 in this case.

3. Use each number as a divisor and verify whether it is a factor by dividing 210 by the number. If the division results in an integer value, then the number is a factor of 210.

4. Finally, collect all the numbers that satisfy the criteria and you will have the factors of 210.

Step-by-step solution

Let's solve the problem step-by-step:

1. Determine the criteria: A number is a factor of 210 if it divides 210 without leaving a remainder.

2. List all the numbers: Starting from 1 up to 210, we have the numbers 1, 2, 3, 4, 5, ..., 209, 210.

3. Use each number as a divisor: Divide 210 by each number and check if the division results in an integer value.

   • 210 ÷ 1 = 210 (integer)
   • 210 ÷ 2 = 105 (integer)
   • 210 ÷ 3 = 70 (integer)
   • 210 ÷ 4 = 52.5 (not an integer)
   • 210 ÷ 5 = 42 (integer)
   • 210 ÷ 6 = 35 (integer)
   • 210 ÷ 7 = 30 (integer)
   • 210 ÷ 8 = 26.25 (not an integer)
   • 210 ÷ 9 = 23.33 (not an integer)
   • 210 ÷ 10 = 21 (integer)
   • 210 ÷ 11 = 19.09 (not an integer)
   • 210 ÷ 12 = 17.5 (not an integer)
   • 210 ÷ 13 = 16.15 (not an integer)
   • 210 ÷ 14 = 15 (integer)
   • 210 ÷ 15 = 14 (integer)
   • 210 ÷ 16 = 13.13 (not an integer)
   • 210 ÷ 17 = 12.35 (not an integer)
   • 210 ÷ 18 = 11.67 (not an integer)
   • 210 ÷ 19 = 11.05 (not an integer)
   • 210 ÷ 20 = 10.5 (not an integer)
   • 210 ÷ 21 = 10 (integer)
   • 210 ÷ 22 = 9.55 (not an integer)
   • 210 ÷ 23 = 9.13 (not an integer)
   • 210 ÷ 24 = 8.75 (not an integer)
   • 210 ÷ 25 = 8.4 (not an integer)
   • 210 ÷ 26 = 8.08 (not an integer)
   • 210 ÷ 27 = 7.78 (not an integer)
   • 210 ÷ 28 = 7.5 (integer)
   • 210 ÷ 29 = 7.24 (not an integer)
   • 210 ÷ 30 = 7 (integer)
   • 210 ÷ 31 = 6.77 (not an integer)
   • 210 ÷ 32 = 6.56 (not an integer)
   • 210 ÷ 33 = 6.36 (not an integer)
   • 210 ÷ 34 = 6.18 (not an integer)
   • 210 ÷ 35 = 6 (integer)
   • 210 ÷ 36 = 5.83 (not an integer)
   • 210 ÷ 37 = 5.68 (not an integer)
   • 210 ÷ 38 = 5.53 (not an integer)
   • 210 ÷ 39 = 5.38 (not an integer)
   • 210 ÷ 40 = 5.25 (not an integer)
   • 210 ÷ 41 = 5.12 (not an integer)
   • 210 ÷ 42 = 5 (integer)
   • 210 ÷ 43 = 4.88 (not an integer)
   • 210 ÷ 44 = 4.77 (not an integer)
   • 210 ÷ 45 = 4.67 (not an integer)
   • 210 ÷ 46 = 4.57 (not an integer)
   • 210 ÷ 47 = 4.47 (not an integer)
   • 210 ÷ 48 = 4.38 (not an integer)
   • 210 ÷ 49 = 4.29 (not an integer)
   • 210 ÷ 50 = 4.2 (not an integer)
   • 210 ÷ 51 = 4.12 (not an integer)
   • 210 ÷ 52 = 4.04 (not an integer)
   • 210 ÷ 53 = 3.96 (not an integer)
   • 210 ÷ 54 = 3.89 (not an integer)
   • 210 ÷ 55 = 3.82 (not an integer)
   • 210 ÷ 56 = 3.75 (not an integer)
   • 210 ÷ 57 = 3.68 (not an integer)
   • 210 ÷ 58 = 3.62 (not an integer)
   • 210 ÷ 59 = 3.56 (not an integer)
   • 210 ÷ 60 = 3.5 (integer)
   • 210 ÷ 61 = 3.44 (not an integer)
   • 210 ÷ 62 = 3.39 (not an integer)
   • 210 ÷ 63 = 3.33 (integer)
   • 210 ÷ 64 = 3.28 (not an integer)
   • 210 ÷ 65 = 3.23 (not an integer)
   • 210 ÷ 66 = 3.18 (not an integer)
   • 210 ÷ 67 = 3.13 (not an integer)
   • 210 ÷ 68 = 3.09 (not an integer)
   • 210 ÷ 69 = 3.04 (not an integer)
   • 210 ÷ 70 = 3 (integer)
   • 210 ÷ 71 = 2.96 (not an integer)
   • 210 ÷ 72 = 2.92 (not an integer)
   • 210 ÷ 73 = 2.88 (not an integer)
   • 210 ÷ 74 = 2.84 (not an integer)
   • 210 ÷ 75 = 2.8 (not an integer)
   • 210 ÷ 76 = 2.76 (not an integer)
   • 210 ÷ 77 = 2.73 (not an integer)
   • 210 ÷ 78 = 2.69 (not an integer)
   • 210 ÷ 79 = 2.66 (not an integer)
   • 210 ÷ 80 = 2.62 (not an integer)
   • 210 ÷ 81 = 2.59 (not an integer)
   • 210 ÷ 82 = 2.56 (not an integer)
   • 210 ÷ 83 = 2.53 (not an integer)
   • 210 ÷ 84 = 2.5 (integer)
   • 210 ÷ 85 = 2.47 (not an integer)
   • 210 ÷ 86 = 2.44 (not an integer)
   • 210 ÷ 87 = 2.41 (not an integer)
   • 210 ÷ 88 = 2.39 (not an integer)
   • 210 ÷ 89 = 2.36 (not an integer)
   • 210 ÷ 90 = 2.33 (not an integer)
   • 210 ÷ 91 = 2.31 (not an integer)
   • 210 ÷ 92 = 2.28 (not an integer)
   • 210 ÷ 93 = 2.26 (not an integer)
   • 210 ÷ 94 = 2.23 (not an integer)
   • 210 ÷ 95 = 2.21 (not an integer)
   • 210 ÷ 96 = 2.19 (not an integer)
   • 210 ÷ 97 = 2.16 (not an integer)
   • 210 ÷ 98 = 2.14 (not an integer)
   • 210 ÷ 99 = 2.12 (not an integer)
   • 210 ÷ 100 = 2.1 (not an integer)
   • 210 ÷ 101 = 2.08 (not an integer)
   • 210 ÷ 102 = 2.06 (not an integer)
   • 210 ÷ 103 = 2.04 (not an integer)
   • 210 ÷ 104 = 2.02 (not an integer)
   • 210 ÷ 105 = 2 (integer)
   • 210 ÷ 106 = 1.98 (not an integer)
   • 210 ÷ 107 = 1.96 (not an integer)
   • 210 ÷ 108 = 1.94 (not an integer)
   • 210 ÷ 109 = 1.92 (not an integer)
   • 210 ÷ 110 = 1.9 (not an integer)
   • 210 ÷ 111 = 1.89 (not an integer)
   • 210 ÷ 112 = 1.88 (not an integer)
   • 210 ÷ 113 = 1.86 (not an integer)
   • 210 ÷ 114 = 1.84 (not an integer)
   • 210 ÷ 115 = 1.83 (not an integer)
   • 210 ÷ 116 = 1.81 (not an integer)
   • 210 ÷ 117 = 1.79 (not an integer)
   • 210 ÷ 118 = 1.78 (not an integer)
   • 210 ÷ 119 = 1.76 (not an integer)
   • 210 ÷ 120 = 1.75 (not an integer)
   • 210 ÷ 121 = 1.74 (not an integer)
   • 210 ÷ 122 = 1.72 (not an integer)
   • 210 ÷ 123 = 1.71 (not an integer)
   • 210 ÷ 124 = 1.69 (not an integer)
   • 210 ÷ 125 = 1.68 (not an integer)
   • 210 ÷ 126 = 1.67 (not an integer)
   • 210 ÷ 127 = 1.65 (not an integer)
   • 210 ÷ 128 = 1.64 (not an integer)
   • 210 ÷ 129 = 1.63 (not an integer)
   • 210 ÷ 130 = 1.62 (not an integer)
   • 210 ÷ 131 = 1.6 (not an integer)
   • 210 ÷ 132 = 1.59 (not an integer)
   • 210 ÷ 133 = 1.58 (not an integer)
   • 210 ÷ 134 = 1.57 (not an integer)
   • 210 ÷ 135 = 1.56 (not an integer)
   • 210 ÷ 136 = 1.54 (not an integer)
   • 210 ÷ 137 = 1.53 (not an integer)
   • 210 ÷ 138 = 1.52 (not an integer)
   • 210 ÷ 139 = 1.51 (not an integer)
   • 210 ÷ 140 = 1.5 (integer)
   • 210 ÷ 141 = 1.49 (not an integer)
   • 210 ÷ 142 = 1.48 (not an integer)
   • 210 ÷ 143 = 1.47 (not an integer)
   • 210 ÷ 144 = 1.46 (not an integer)
   • 210 ÷ 145 = 1.45 (not an integer)
   • 210 ÷ 146 = 1.44 (not an integer)
   • 210 ÷ 147 = 1.43 (not an integer)
   • 210 ÷ 148 = 1.42 (not an integer)
   • 210 ÷ 149 = 1.41 (not an integer)
   • 210 ÷ 150 = 1.4 (integer)
   • 210 ÷ 151 = 1.39 (not an integer)
   • 210 ÷ 152 = 1.38 (not an integer)
   • 210 ÷ 153 = 1.37 (not an integer)
   • 210 ÷ 154 = 1.36 (not an integer)
   • 210 ÷ 155 = 1.35 (not an integer)
   • 210 ÷ 156 = 1.34 (not an integer)
   • 210 ÷ 157 = 1.34 (not an integer)
   • 210 ÷ 158 = 1.33 (not an integer)
   • 210 ÷ 159 = 1.32 (not an integer)
   • 210 ÷ 160 = 1.31 (not an integer)
   • 210 ÷ 161 = 1.31 (not an integer)
   • 210 ÷ 162 = 1.3 (not an integer)
   • 210 ÷ 163 = 1.29 (not an integer)
   • 210 ÷ 164 = 1.28 (not an integer)
   • 210 ÷ 165 = 1.27 (not an integer)
   • 210 ÷ 166 = 1.27 (not an integer)
   • 210 ÷ 167 = 1.26 (not an integer)
   • 210 ÷ 168 = 1.25 (not an integer)
   • 210 ÷ 169 = 1.24 (not an integer)
   • 210 ÷ 170 = 1.24 (not an integer)
   • 210 ÷ 171 = 1.23 (not an integer)
   • 210 ÷ 172 = 1.22 (not an integer)
   • 210 ÷ 173 = 1.21 (not an integer)
   • 210 ÷ 174 = 1.21 (not an integer)
   • 210 ÷ 175 = 1.2 (integer)
   • 210 ÷ 176 = 1.19 (not an integer)
   • 210 ÷ 177 = 1.19 (not an integer)
   • 210 ÷ 178 = 1.18 (not an integer)
   • 210 ÷ 179 = 1.17 (not an integer)
   • 210 ÷ 180 = 1.17 (not an integer)
   • 210 ÷ 181 = 1.16 (not an integer)
   • 210 ÷ 182 = 1.15 (not an integer)
   • 210 ÷ 183 = 1.15 (not an integer)
   • 210 ÷ 184 = 1.14 (not an integer)
   • 210 ÷ 185 = 1.14 (not an integer)
   • 210 ÷ 186 = 1.13 (not an integer)
   • 210 ÷ 187 = 1.12 (not an integer)
   • 210 ÷ 188 = 1.12 (not an integer)
   • 210 ÷ 189 = 1.11 (not an integer)
   • 210 ÷ 190 = 1.11 (not an integer)
   • 210 ÷ 191 = 1.1 (not an integer)
   • 210 ÷ 192 = 1.09 (not an integer)
   • 210 ÷ 193 = 1.09 (not an integer)
   • 210 ÷ 194 = 1.08 (not an integer)
   • 210 ÷ 195 = 1.08 (not an integer)
   • 210 ÷ 196 = 1.07 (not an integer)
   • 210 ÷ 197 = 1.07 (not an integer)
   • 210 ÷ 198 = 1.06 (not an integer)
   • 210 ÷ 199 = 1.06 (not an integer)
   • 210 ÷ 200 = 1.05 (not an integer)
   • 210 ÷ 201 = 1.05 (not an integer)
   • 210 ÷ 202 = 1.04 (not an integer)
   • 210 ÷ 203 = 1.04 (not an integer)
   • 210 ÷ 204 = 1.03 (not an integer)
   • 210 ÷ 205 = 1.03 (not an integer)
   • 210 ÷ 206 = 1.02 (not an integer)
   • 210 ÷ 207 = 1.02 (not an integer)
   • 210 ÷ 208 = 1.01 (not an integer)
   • 210 ÷ 209 = 1.01 (not an integer)
   • 210 ÷ 210 = 1 (integer)

4. Collect all the numbers that satisfy the criteria: The numbers that divide 210 without leaving a remainder are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

Pair Factors and Negative Pair Factors of Factors of 210

Pair factors are the factors that can be multiplied together to give the original number. For the factors of 210, the pair factors are:

• 1 × 210 = 210
• 2 × 105 = 210
• 3 × 70 = 210
• 5 × 42 = 210
• 6 × 35 = 210
• 7 × 30 = 210
• 10 × 21 = 210
• 14 × 15 = 210

Negative pair factors are the pair factors with one positive and one negative factor. Since 210 is a positive number, the negative pair factors are:

• (-1) × (-210) = 210
• (-2) × (-105) = 210
• (-3) × (-70) = 210
• (-5) × (-42) = 210
• (-6) × (-35) = 210
• (-7) × (-30) = 210
• (-10) × (-21) = 210
• (-14) × (-15) = 210

Prime Factorisation of 210

Prime factorisation is the process of expressing a number as a product of its prime factors. To find the prime factorisation of 210, we divide it by prime numbers until we can no longer divide.

Dividing 210 by 2 gives us 105. Dividing 105 by 3 gives us 35. Dividing 35 by 5 gives us 7. Since 7 is a prime number, we stop here.

Therefore, the prime factorisation of 210 is 2 × 3 × 5 × 7.

Solved Examples

1. Find the factors of 210.

   Solution: The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

2. Determine the pair factors of 210.

   Solution: The pair factors of 210 are 1 × 210, 2 × 105, 3 × 70, 5 × 42, 6 × 35, 7 × 30, 10 × 21, and 14 × 15.

3. Find the prime factorisation of 210.

   Solution: The prime factorisation of 210 is 2 × 3 × 5 × 7.

Factors in Mathematics

In mathematics, factors are numbers that divide a given number without leaving a remainder. They play a crucial role in various mathematical concepts, such as prime factorisation, finding common factors, and solving equations.

Symbols Used to Represent Factors

The symbol used to represent factors is ":" or "|". For example, we can represent the factors of 210 as 1:210, 2:105, 3:70, and so on.

Types of Factors

There are two types of factors: prime factors and composite factors. Prime factors are the factors that are prime numbers, while composite factors are the factors that are composite numbers.

FAQs on Factors of 210

Question: What are the factors of 210? Answer: The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.