Factors of 125: Pair factors and Prime Factors – Mindspark

Factors of 125

The numbers that divide 125 completely are called its factors. That’s why 1, 5, 25 and 125 are the required factors as per the definition.

In other words, if two whole numbers are multiplied with each other, and the result is 125, then both the whole numbers are the factors of 125.

For example,

1 × 125 = 125

5 × 25 = 125

so 1, 5, 25, and 125 are the required factors.

How To Find the Factors of 125?

Factors of 125 are the numbers that divide it wholly and leave zero as a remainder. Every number is completely divisible by 1 and the number itself. So, the two factors will be 1 and the number itself, which is 125. 

To find other factors, we will do the divisibility test.

• Using the divisibility rules, we find that 125 is not divisible by 2, 3 or 4, but it is divisible by 5.

• So, divide 125 with 5. 125 ÷ 5 = 25, we get 25 as the quotient and zero as the remainder.

• Since the quotient is 25 and the remainder is 0. So, 125 will be completely divisible by the quotient 25 also. 
• 125 is not wholly divisible by any other number apart from 1, 5, 25 and 125.
• Therefore, the factors are 1, 5, 25 and 125.

Pair Factors of 125

We will have to find pairs of such numbers whose product is 125. These two pairs are – 

1 × 125 = 125

5 × 25 = 125

Hence, the pair factors are (1, 125) and (5, 25)

Similarly, the negative pair factors will be (-1, -125) and (-5, -25). It is because the product of two negative numbers is a positive number.

Prime Factorization of 125 Using Division Method

To find the prime factors, we will have to divide 125 by prime numbers till the quotient obtained is 1. Let’s understand how. 

• The smallest prime factor of 125 is 5. So divide 125 by 5, and we get:

            \frac{125}{5}=25

• The smallest prime factor of 25 is also 5. Now divide 25 by 5, and we get:

          \frac{25}{5}=5

• Now divide 5 by the smallest prime factor of 5, i.e. 5, and we get:

          \frac{5}{5}=1 

• Now, we can’t divide 1 by any other prime numbers.
  
• Therefore, prime factorization of 125 is equal to 5 x 5 x 5.

Examples

1. Find the factor of 125 among the numbers given below –
20, 25, 30, 35

The number 25 divides the number 125 completely without leaving any remainder. Therefore 25 is the factor of 125.