Factors of 162

NOVEMBER 08, 2023

Factors of 162

Factors are numbers that can be multiplied together to obtain a given number. In this blog, we will explore the factors of 162 and discuss various aspects related to them.

Answer to Factors of 162

The factors of 162 are: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.

How to solve the problem: hints

To find the factors of 162, we can follow these steps:

  1. Determine the criteria for judging whether a number is a factor. A number is a factor of 162 if it divides 162 without leaving a remainder.

  2. List all the numbers starting from 1 and going up to the given number, which is 162 in this case.

  3. Use each number as a divisor and verify whether it is a factor by dividing 162 by the number. If the division is exact, without any remainder, then the number is a factor.

  4. Finally, collect all the numbers that are factors of 162.

Let's now provide a concise step-by-step solution using math expressions.

Step-by-step solution

  1. The criteria for judging whether a number is a factor of 162 is that it should divide 162 without leaving a remainder.

  2. List all the numbers from 1 to 162: 1, 2, 3, 4, 5, ..., 160, 161, 162.

  3. Use each number as a divisor and verify whether it is a factor by performing the division:

    • 162 ÷ 1 = 162 (exact division, so 1 is a factor)
    • 162 ÷ 2 = 81 (exact division, so 2 is a factor)
    • 162 ÷ 3 = 54 (exact division, so 3 is a factor)
    • 162 ÷ 4 = 40.5 (not an exact division, so 4 is not a factor)
    • 162 ÷ 5 = 32.4 (not an exact division, so 5 is not a factor)
    • ...
    • 162 ÷ 160 = 1.0125 (not an exact division, so 160 is not a factor)
    • 162 ÷ 161 = 1.0062 (not an exact division, so 161 is not a factor)
    • 162 ÷ 162 = 1 (exact division, so 162 is a factor)
  4. Collect all the numbers that are factors of 162: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.

Pair Factors and Negative Pair Factors of Factors of 162

The pair factors of 162 are the pairs of numbers that multiply together to give 162. For example, the pair factors of 162 are (1, 162), (2, 81), (3, 54), (6, 27), (9, 18), and (18, 9).

The negative pair factors of 162 are the pairs of numbers, one positive and one negative, that multiply together to give 162. For example, the negative pair factors of 162 are (-1, -162), (-2, -81), (-3, -54), (-6, -27), (-9, -18), and (-18, -9).

Prime Factorisation of 162

Prime factorisation is the process of expressing a number as a product of its prime factors. The prime factors of 162 are the prime numbers that divide 162 without leaving a remainder.

The prime factorisation of 162 is 2 × 3^4, where 2 is a prime number and 3 is also a prime number. This can be written as 2 × 3 × 3 × 3 × 3.

Solved Examples

  1. Example: Find the factors of 162.

    Solution: The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.

  2. Example: Determine the pair factors of 162.

    Solution: The pair factors of 162 are (1, 162), (2, 81), (3, 54), (6, 27), (9, 18), and (18, 9).

  3. Example: Calculate the prime factorisation of 162.

    Solution: The prime factorisation of 162 is 2 × 3^4.

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 by writing the numbers next to each other. For example, the factors of 162 can be represented as 1 × 2 × 3 × 6 × 9 × 18 × 27 × 54 × 81 × 162 or simply as 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.

Types of Factors

There are different types of factors, including prime factors, composite factors, and negative factors.

  • Prime factors are the prime numbers that divide a given number without leaving a remainder.
  • Composite factors are the composite numbers that divide a given number without leaving a remainder.
  • Negative factors are the pairs of numbers, one positive and one negative, that multiply together to give the given number.

FAQs on Factors of 162

Question: Factors of 162? The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.