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Factors of 25

 

The factors, which when divided to 25 do not leave any remainder, are known as prime factors of 25. This means, 25 must be completely divisible by such a number that it does not leave any remainder.

  • The factors of a number are finite. It means, universally, that number will have specific factors only.
  • Only the composite numbers can be factored in because they are made from the product of two or more numbers.
  • Only integers and whole numbers can be factored in and will have factors.
  • Every factor of a number is equal to less than the number itself.

The integer 25 can be divided only into three numbers – 1, 5 and 5. It means, the product of 5 and 5 only will result in 25. Therefore, the largest prime factor of 25 is 5, which is also a prime number. However, 25 will have the following categories of factors-

Positive factors: 1, 5

Prime factors: 5, 5, which are not further divisible.

Negative factors: -5, -5

Prime factorization of 25 = 5 x 5 = 5²

How to find the factors of 25?

The factors of 25 can be found by two methods – Prime factorization method and Long-division method.

Prime factorization method to find factors of 25

The prime factorization method is the most common method to represent 25 or any other number. Its other form, the prime factor tree method, is a visual method to represent factors of 25. It helps in determining various prime factors of 25. A factor tree is not unique for a given number. We can express 25 as 5 x 5.

We need to divide 25, from the smallest number to the largest number so that it completely divides the number-

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  • With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 25, which is an odd number. It is not divisible by 2. In other words, we need to look for another number greater than 2 that can divide 25 completely.
  • 5 divides the number 25, therefore, it is the smallest prime factor of 25. However, 5 is also the largest factor of 25 as no other number divides 25 completely.
  • 25 ÷ 5 = 5. We need to repeat the steps with other numbers until we get the remainder of 0.
  • 5 is not further divisible by any other number other than 5 itself.
  • 5 ÷ 5 = 1. Here, we get remainder 1. After this, our process is completed, and we get factors of 25.

Prime factorization of 25 using the prime factorization method is 5 x 5 = 5²

Example 1:

What are the common factors of 25 and 125?

Solution:

The factors of 25 are 1 and 5.

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

Thus, the common factors of 25 and 125 are 1 and 5.

Example 2:

What are the common factors of 25, 125 and 225?

Solution:

The factors of 25 are 1 and 5.

The factors of 125 are 1, 5, and 25. The factors of 225 are 1, 3, 5, 9, 15, 25, 45, and 75.

Thus, the common factors of 25, 125 and 225 are 1 and 5.

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