Factors of 50

Factors of 50

Factors are numbers that can be multiplied together to get a given number. In this blog, we will explore the factors of 50 and understand their properties.

Answer to Factors of 50

The factors of 50 are: 1, 2, 5, 10, 25, and 50.

How to solve the problem: hints

1. The criteria for judging whether a number is a factor of 50 is that it should divide 50 without leaving a remainder.
2. List all the numbers from 1 to 50.
3. Use each number as a divisor and verify whether it divides 50 without leaving a remainder.
4. Finally, the numbers that satisfy the criteria are the factors of 50.

Step-by-step solution

1. List all the numbers from 1 to 50: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
2. Use each number as a divisor and verify whether it divides 50 without leaving a remainder:
   • 1 is a factor of 50 (50 ÷ 1 = 50).
   • 2 is a factor of 50 (50 ÷ 2 = 25).
   • 3 is not a factor of 50 (50 ÷ 3 = 16 remainder 2).
   • 4 is not a factor of 50 (50 ÷ 4 = 12 remainder 2).
   • 5 is a factor of 50 (50 ÷ 5 = 10).
   • 6 is not a factor of 50 (50 ÷ 6 = 8 remainder 2).
   • 7 is not a factor of 50 (50 ÷ 7 = 7 remainder 1).
   • 8 is not a factor of 50 (50 ÷ 8 = 6 remainder 2).
   • 9 is not a factor of 50 (50 ÷ 9 = 5 remainder 5).
   • 10 is a factor of 50 (50 ÷ 10 = 5).
   • 11 is not a factor of 50 (50 ÷ 11 = 4 remainder 6).
   • 12 is not a factor of 50 (50 ÷ 12 = 4 remainder 2).
   • 13 is not a factor of 50 (50 ÷ 13 = 3 remainder 11).
   • 14 is not a factor of 50 (50 ÷ 14 = 3 remainder 8).
   • 15 is not a factor of 50 (50 ÷ 15 = 3 remainder 5).
   • 16 is not a factor of 50 (50 ÷ 16 = 3 remainder 2).
   • 17 is not a factor of 50 (50 ÷ 17 = 2 remainder 16).
   • 18 is not a factor of 50 (50 ÷ 18 = 2 remainder 14).
   • 19 is not a factor of 50 (50 ÷ 19 = 2 remainder 12).
   • 20 is not a factor of 50 (50 ÷ 20 = 2 remainder 10).
   • 21 is not a factor of 50 (50 ÷ 21 = 2 remainder 8).
   • 22 is not a factor of 50 (50 ÷ 22 = 2 remainder 6).
   • 23 is not a factor of 50 (50 ÷ 23 = 2 remainder 4).
   • 24 is not a factor of 50 (50 ÷ 24 = 2 remainder 2).
   • 25 is a factor of 50 (50 ÷ 25 = 2).
   • 26 is not a factor of 50 (50 ÷ 26 = 1 remainder 24).
   • 27 is not a factor of 50 (50 ÷ 27 = 1 remainder 23).
   • 28 is not a factor of 50 (50 ÷ 28 = 1 remainder 22).
   • 29 is not a factor of 50 (50 ÷ 29 = 1 remainder 21).
   • 30 is not a factor of 50 (50 ÷ 30 = 1 remainder 20).
   • 31 is not a factor of 50 (50 ÷ 31 = 1 remainder 19).
   • 32 is not a factor of 50 (50 ÷ 32 = 1 remainder 18).
   • 33 is not a factor of 50 (50 ÷ 33 = 1 remainder 17).
   • 34 is not a factor of 50 (50 ÷ 34 = 1 remainder 16).
   • 35 is not a factor of 50 (50 ÷ 35 = 1 remainder 15).
   • 36 is not a factor of 50 (50 ÷ 36 = 1 remainder 14).
   • 37 is not a factor of 50 (50 ÷ 37 = 1 remainder 13).
   • 38 is not a factor of 50 (50 ÷ 38 = 1 remainder 12).
   • 39 is not a factor of 50 (50 ÷ 39 = 1 remainder 11).
   • 40 is not a factor of 50 (50 ÷ 40 = 1 remainder 10).
   • 41 is not a factor of 50 (50 ÷ 41 = 1 remainder 9).
   • 42 is not a factor of 50 (50 ÷ 42 = 1 remainder 8).
   • 43 is not a factor of 50 (50 ÷ 43 = 1 remainder 7).
   • 44 is not a factor of 50 (50 ÷ 44 = 1 remainder 6).
   • 45 is not a factor of 50 (50 ÷ 45 = 1 remainder 5).
   • 46 is not a factor of 50 (50 ÷ 46 = 1 remainder 4).
   • 47 is not a factor of 50 (50 ÷ 47 = 1 remainder 3).
   • 48 is not a factor of 50 (50 ÷ 48 = 1 remainder 2).
   • 49 is not a factor of 50 (50 ÷ 49 = 1 remainder 1).
   • 50 is a factor of 50 (50 ÷ 50 = 1).
3. Finally, the factors of 50 are: 1, 2, 5, 10, 25, and 50.

Pair Factors and Negative Pair Factors of Factors of 50

The pair factors of 50 are the factors that can be multiplied together to get 50. In this case, the pair factors are: (1, 50) and (2, 25).

The negative pair factors of 50 are the pair factors with one negative and one positive number. In this case, the negative pair factors are: (-1, -50), (-2, -25), (1, -50), and (2, -25).

Prime Factorisation of 50

Prime factorisation is the process of expressing a number as a product of its prime factors. The prime factors of 50 are 2 and 5. Therefore, the prime factorisation of 50 is 2 × 5 × 5, or in exponential form, 2^1 × 5^2.

Solved Examples

1. Find the factors of 50.

   • The factors of 50 are: 1, 2, 5, 10, 25, and 50.

2. Determine the pair factors of 50.

   • The pair factors of 50 are: (1, 50) and (2, 25).

3. Calculate the negative pair factors of 50.

   • The negative pair factors of 50 are: (-1, -50), (-2, -25), (1, -50), and (2, -25).

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

In mathematics, factors are often represented using the multiplication symbol (×) or a dot (·). For example, the factors of 50 can be written as 1 × 50, 2 × 25, or 1 · 50, 2 · 25.

Types of Factors

There are different types of factors, including prime factors, composite factors, pair factors, and negative pair factors. Prime factors are numbers that are only divisible by 1 and themselves, while composite factors have more than two factors. Pair factors are two numbers that can be multiplied together to get a given number, and negative pair factors are pair factors with one negative and one positive number.

FAQs on Factors of 50

Question: Factors of 50? The factors of 50 are: 1, 2, 5, 10, 25, and 50.