Factors of 625

The factors of 625 are the numbers that divide 625 completely, without leaving any remainder. The pair factors of 625 can be represented in both positive form and negative form. For example, the pair factor of 625 is expressed as (1, 625) or (-1, -625). If we multiply -1 and -625, it will result in the original number 625. In this article, we will learn the factors of 625, positive and negative pair factors of 625, how to find the prime factors of 625 using the prime factorization method and solved examples in detail.

Table of Contents:

• Factors of 625
• Pair Factors of 625
• Factors of 625 by Division Method
• Prime Factorisation of 625
• Solved Examples
• Practice Problems
• FAQs

What are the Factors of 625?

In Mathematics, the factors of a number are the numbers that divide the given number exactly without leaving any remainder. Thus, the factors of 625 are the numbers that divide 625 evenly and leave the remainder value 0. Thus, the factors of 625 are 1, 5, 25, 125, and 625. Similarly, the negative factors of 625 are -1, -5, -25, -125, and -625.

Pair Factors of 625

The pair factor of 625 is a pair of numbers that are multiplied together resulting in the original number 625. As the number 625 is a composite number, it should have more than one pair factor. Hence, the positive and negative pair factors of 625 are as follows:

Positive Pair Factors of 625:

Therefore, the positive pair factors of 625 are (1, 625), (5, 125), and (25, 25).

Negative Pair Factors of 625:

Therefore, the negative pair factors of 625 are (-1, -625), (-5, -125), and (-25, -25).

Factors of 625 by Division Method

In this method, the factors of 625 are found by dividing the number 625 by different integer numbers. If the integer divides the number 625 completely, then the integer is a factor of 625. Go through the procedure given below to find the factors of 625 using the division method.

• 625/1 = 625 (Factor is 1 and Remainder is 0)
• 625/5 = 125 (Factor is 5 and Remainder is 0)
• 625/25 = 25 (Factor is 25 and Remainder is 0)
• 625/125 = 5 (Factor is 125 and Remainder is 0)
• 625/625 = 1 (Factor is 1 and Remainder is 0)

So, the factors of 625 are 1, 5, 25, 125, and 625.

Note: If we divide 625 by any numbers other than 1, 5, 25, 125, and 625, it leaves a remainder of some number.

Prime Factorisation of 625

In the prime factorisation of 625, the number 625 is written in the form of multiple of the prime factors of 625. Thus, the process of finding the prime factors of 625 using the prime factorisation method is given below.

Consider a pair factor of 625, say (1, 625)

Here, the number 1 is neither prime nor composite. Hence, keep the number as it is.

Now, take the number 625, and find two numbers which, on multiplication, results in the original number 625.

Thus, 625 is written as the product of 25 and 25. But still, 25 is a composite number, which can be further split into its prime factors.

We know that 25 is written as 5 × 5 where 5 is a prime number.

Therefore,

625 = 25 × 25

625 = 5 × 5 × 5 × 5.

Therefore, the prime factorisation of 625 is 5 × 5 × 5 × 5 or 5⁴.

Video Lesson on Prime Factors

Solved Examples

Example 1:

Determine the common factors of 625 and 25.

Solution:

The factors of 625 are 1, 5, 25, 125, and 625.

The factors of 25 are 1, 5 and 25

Thus, the common factors of 625 and 25 are 1, 5 and 25.

Example 2:

Find the common factors of 625 and 623.

Solution:

Factors of 625 = 1, 5, 25, 125, and 625.

Factors of 623 = 1, 7, 89 and 623.

Hence, the common factor of 625 and 623 is 1.

Example 3:

What are the common factors of 625 and 659?

Solution:

The factors of 625 are 1, 5, 25, 125, 625.

The factors of 659 are 1, 659.

Since the number 659 is a prime number, the common factor of 625 and 659 is 1.

Practice Problems

1. What is the sum of factors of 625?
2. What is the greatest common factor for 125 and 625?
3. Determine the common factors of 625 and 256?

To learn more factors of a number, stay tuned with BYJU’S – The Learning App and download the app to learn more Maths-related concepts easily by exploring more videos.