FACTORS OF 25 WITH EXAMPLES AND FAQ

FACTORS OF 25

Any number is a factor of a number if it divides the given number without leaving any remainder behind. For example, 2 is a factor of 4, 5 is a factor of 20, etc.

25 is a composite number and hence it has factors that are other than 1 and itself. If a number can completely divide 25 without leaving a remainder, then that number is a factor of 25.  

The factors of 25 are 1, 5 and 25.

Here, 1 is the smallest factor and 25 itself is its biggest factor.

How to determine factors of 25?

Let’s find the factors by simply dividing 25 by all the numbers starting from 1 to 25 and see which number divides 25 without leaving a remainder. We see that when 25 is divided by 1,  5 and 25 the remainder is 0. Hence 1, 5 and 25 are its factors.

Prime Factorization of 25

We divide 25 by prime numbers in this method. In this method, we will continue division with the quotient if it’s a composite number till the final quotient is 1.

The prime factors can be obtained by (a) Division Method or (b) Factor Tree Method.

(a) Prime Factorization using Division Method

We divide the number 25 by the smallest prime number which doesn’t leave a remainder. The quotient obtained is divided repeatedly by the smallest prime number until the last quotient obtained is 1.

Divide 25 by the prime number 5, 

25 ÷ 5 = 5, and continue similarly

5 ÷ 5 = 1

Hence the prime factorization of 25 is 5 × 5 × 1.

(b) Prime Factorization using the Factor Tree Method

We need to find the prime factorization of 25, hence, the root of the factor tree is 25. We can write the pair of factors as the branch of 25. The factor tree ends at a prime factor. 

Factor tree of 25

The factor tree ends at 5 since it is a prime number.

∴ prime factorization of 25 is 5 × 5 × 1.

Factors of 25 in Pairs

A factor pair includes the set of two numbers whose product will give the number as the product. Factor pairs of 25 are:

1 × 25 = 25, Hence the factor pair is (1, 25)

5 × 5 = 25, Hence the factor pair is (5, 5)

The product of two negative numbers is positive. Hence, the negative factor pairs of 25 are:

(-1) × (- 25) = 25, Hence the factor pair is (-1, -25).

(-5) × (-5) = 25, Hence the factor pair is (-5, -5).

Examples

Example 1: Do 25 and 35 have any factors in common?

Solution: There are four factors of 35 which are:

35 ÷ 1 = 35

35 ÷ 5 = 7

35 ÷ 7 = 5

35 ÷ 35 = 1

Hence, the factors of 35 are: 1, 5, 7 and 35.

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

Therefore, 25 and 35 have 1 and 5 as common factors.

Example 2: Find the sum of all the factors of 25.

Solution:

We know the factors of 25 are: 1, 5 and 25.

∴ The sum of all the factors is = 1+ 5 + 25 = 31.