Factors Of 25 | With Easy Division and Prime Factorization

Factors Of 25

Factors of 25 are mixtures of numbers that, when multiplied together, result in 25. If we divide a number by its factor, the resultant quotient is a whole number. 

It can be expressed both positively and negatively, but it cannot be expressed as a decimal or fraction. Similarly, you can also describe pair factors of 25 positively or negatively. 

Taking 25 as an example, the pair factor can be (1, 25) or (-1, 25). In the case of multiplying -1 and -5, the answer will be 25. The purpose of this article is to discuss the factors of 25 as well as the methods for finding pair factors and prime factors using the prime factorization method.

What are the Factors of 25?

A 25 factor is the number that divides 25 exactly without leaving a remainder. In addition to 1 and 25 being composite numbers, 25 has other factors as well. In total, 25 have factors 1, 5, and 25. 

Similarly, the negative factors of 25 are -1, -5, and -25. 

• Factors of 25: 1, 5, and 25.
• Prime Factorization of 25: 5 × 5 or 5².

What are the Factors Of -25?

Factors of -25: -1, -5, and -25.

We can get -25 by having (-1, 25) and (-5, 5) as a pair of factors. Similarly, we can also get -24 by having (1, -25) and (5, -5) as a pair of factors.

Pair Factors of 25

A pair factor of 25 is a pair of numbers that, when multiplied, produces an original number. Positive or negative pair factors of 25 are possible, as discussed above. Hence, here are positive and negative pair factors of 25:

Positive Pair Factors of 25:

Negative Pair Factors of 25:

Factors of 25 by Division Method

Using the division method, it is easy to find the factors of 25. 25 is divided into different integers using this method. The integers are factors of 25 if they divide 25 exactly and leave a remainder of 0. Here is how we can find the factors of 25 using the division method.

• 25/1 = 25  (Factor is 1 and Remainder is 0)
• 25/5 = 5    (Factor is 5 and Remainder is 0)
• 25/25 = 1  (Factor is 25 and Remainder is 0)

As a result, 25 has factors 1, 5, and 25.

Note: When we divide 25 by any number other than 1, 5, and 25, we get 0 as a result, so these are not factors of 25.

Prime Factorization of 25

It is a composite number. We can now determine its prime factors.

• To begin, divide 25 by the smallest prime factor, i.e., 2

25 ÷ 2 = 12.5

          In this case, 2 is not a prime factor of 25.

• Next, we will look at the next prime number, i.e., 3

25 ÷ 3 = 8.33

           Hence, 3 cannot be a prime factor of 25.

• Continue dividing this prime number until you arrive at a fraction of 1 as the output.

25 ÷ 5 = 5

5 ÷ 5 = 1

• As a result of the division process, we have received 1 and can no longer proceed. Consequently, the prime factors of 25 are 5 × 5 or 5², where 5 is a prime number.

Examples

Example 1:

Calculate the factors of 25 and 24.

Solution:

25 is made up of factors 1, 5, and 25.

Factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24.

As a result, 25 and 24 have 1 common factor.

Example 2:

Determine factors 25 and 28.

Solution:

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

1, 2, 4, 7, 14, and 28 are factors of 28.

Therefore, 25 and 28 have a common factor of 1.

Example 3:

Identify the factor of 25 and 3.

Solution:

25 has three factors: 1, 5, and 25.

1 and 3 are the factors of 3.

Since 3 is a prime number, 25 and 3 have a common factor of 1.

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