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Factors of 125 | Prime Factorization of 125 | Factor Tree of 125

Written by Prerit Jain

Updated on: 15 Feb 2023

Factors of 125 | Prime Factorization of 125 | Factor Tree of 125

Factors of 125 | Prime Factorization of 125 | Factor Tree of 125

The factors of a number are the numbers that can divide the given number completely and evenly. The numbers can have both negative and positive pair factors and the factors of a number can be found by using the basic prime factorization method, division method, and factor tree method. From this article, you can know about the factors of 125 and the various ways to find out the prime factors of 125 too.

What Are the Factors of 125?

The factors of the given number 125 are the numbers that can completely and evenly divide the given number 125 without any decimal points. Based on the count of the number of factors, the numbers can be divided into prime numbers and composite numbers. The number 125 is a composite number as it has more than two factors. And those factors of 125 are 1, 5, 25, and 125.

Factors of 125: 1, 5, 25, and 125.
Negative Factors of 125: -1, -5, -25, and -125.
Prime Factorization of 125: 5 x 5 x 5
Pair Factors of 125: (1, 125) and (5, 25)
Prime Factors of 125: 5
Sum of Factors of 125: 156
Sum of Prime Factors of 125: 5
Factors of 125

What Are the Factors of 125 in Pairs?

The factors of a number can be both positive and negative. The numbers which on multiplying with each other should get the number 125 as its resultant value are known as the pair factors of that number.

Positive Pair Factors of 125

The positive pair factors of 125 are (1, 125) and (5, 25).

Positive Pair Factors of 125

Negative Pair Factors of 125

The negative pair factors of 125 are (-1, -125) and (-5, -25).

Negative Pair Factors of 125

What Is the Prime Factorization Method of 125?

Prime factorization is a method used to find out the prime factors of the given numbers. It’s always very much important to check whether the given number is a composite number or a prime number before applying this method to a number. The steps involved in this process are as follows:

  • Step 1: Let’s place 125 at the top and divide it by the smallest number that can divide the given number 125 and that number is 5.
    125 ÷ 5 = 25
  • Step 2: Now the quotient 25 is divisible again by 5.
    25 ÷ 5 = 5
  • Step 3: Now again the number 5 is divisible by 5.
    5 ÷ 5 = 1
  • Step 4: As now the quotient is 1, it’s not further divisible.

Therefore, the prime factor of 125 is 5. The pictorial representation of 125 is given below:

Prime Factorization of 125

How to Find Factors of 125 Through Division Method?

The division Method is used to find the factors of the given number by dividing each number by that given number, starting from 1 till the given number. The following is the process involved in it:

  • 125 ÷ 1 = 125
  • 125 ÷ 5 = 25
  • 125 ÷ 25 = 5
  • 125 ÷ 125 =1

Therefore, the factors of 125 are 1, 5, 25, and 125.

What Is the Factor Tree of 125?

A factor tree is another method used to find out the prime factors of 125. It also conveys the ways through which the prime factors of number can be derived. The following are the steps involved in that process.

  • Step 1: Let’s place the number 125 at the top and put its first set of pair factors in its branches. And those numbers are a and 25.
  • Step 2: Now, the number 25 has its pair factor, so place them in the branches of 25. That numbers are 5 and 5.
  • Step 3: In this case, the number 5 is a prime number and it doesn’t have factors apart from itself and one. So, now let’s circle the prime numbers in the factor tree.

Therefore, the prime factors of 125 are 5 x 5 x 5. And also the number 125 is a perfect cube number. The given below image shows the factor tree of 125.

Factor tree of 125

Solved Examples of 125

What are the factors of 125?
The factors of 125 are 1, 5, 25, and 125.

What is the sum of prime factors of 125?
The sum of the prime factors of 125 is 156.

What is the prime factor of 125?
The prime factor of 125 is 5.

Frequently Asked Questions

Is 125 a prime number?
No, 125 is not a prime number as it has more than two factors.

What are multiples of 125?
The first 10 multiples of 125 are 125, 250, 375, 500, 625, 750, 875, 1000, 1125, and 1250.

Does 125 have a cube root?
Yes, the number 125 is a perfect cube. It is 5 x 5 x 5.

What is square of 125?
The square of 125 is 15,625.

What are all the factors of 125?
The factors of 125 are 1, 5, 25, and 125.

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Prerit Jain

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