Factors of 125 are those whole numbers that divide the original number evenly. means that there is no remainder after dividing 125 by its factor. therefore, the factor of any number is the proper divisor of the real number. for example, 5 is the factor of 125 because when we divide 125 by 5 we get;

125 divided by 5 â‡’ 125 Ã· 5 = 25

thus, we get an integer as a quotient after division.

In the same way, we can find the other factors of 125 here in this article. In addition, we will come across the pair factors of 125. These pair factors result in original numbers when multiplied together. the prime factors of 125 are the primes that can evenly divide the original number.

## how to find the factors of 125?

The factors of 125 are the numbers that divide the original number, leaving no remainder. We will start by dividing 125 by the smallest natural number 1. As we know, 125 is an odd number, therefore it cannot be divided by any even number.

125 Ã· 1 = 125

125 Ã· 5 = 25

125 Ã· 25 = 5

125 Ã· 125 = 1

If we divide 125 by any other number between 1 and 125, then the quotient will be a fraction and not a whole number. for example, 125 divided by 10 is 12.5.

therefore, we can conclude that only 1, 5, 25 and 125 are the factors of 125.

### more factors

- factors of 75
- factors of 27
- factors of 25
- factors of 120
- factors of 215

**factors of pairs of 125**

To find the pair factors of 125, we need to find the product of the two numbers, so that we get the original number as 125.

1 Ã— 125 = 125

5 Ã— 25 = 125

thus, the pair factors ** are **(1, 125) and (5, 25). these are the positive pair factors.

Similarly, if we consider factors of negative pairs, the multiplication of two negative factors will result in a positive value.

-1 Ã— -125 = 125

-5 Ã— -25 = 125

thus, the **negative pair factors are **(-1, -125) and (-5, -25).

## prime factorization of 125

To find the prime factors of 125 we need to divide it by prime numbers until the remainder is 1.

**step 1: **dividing 125 by the smallest prime factor, which is 5, we get;

125/5 = 25

**step 2:** again divide 25 by the smallest prime factor, 5, to get;

5/5 = 1

**Step 3:** We can no longer divide 1 by prime factors. therefore,

## video lesson on prime factors

## worked examples

**p.1: if there are 125 books to distribute among 25 students in a class. How many books does each student receive?**

solution: given,

number of books = 125

number of students in class = 25

each student will get = 125/25 = 5 books

**p.2: what is the sum of all the factors of 125?**

Solution: The factors of 125 are 1, 5, 25, and 125.

sum = 1+5+25+125 = 156

thus, 156 is the required sum.

**p.3: What are the common factors of 25 and 125?**

Answer: To find the common factors, we need to write the factors of each of the given numbers.

Since 25 and 125 are composite numbers, they will have more than two factors.

25â†’ 1.5 and 25

125 â†’ 1,5,25 and 125.

we can see, the common factors are 1, 5 and 25.

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