Factors of 75

The factors of 75 are the numbers that produce the result 75 when two numbers are multiplied together. Pair factors of 75 are the whole numbers which could be either positive or negative but not a fraction or decimal number.  To find the factors of a number, 75, we will use the division method and the factorization method. In the factorization method, first consider the numbers 1 and 75, and continue with finding the other pair of numbers, which will result in 75. To understand this method in a better way, read the below article to find the factor of 75 in pairs. Also, the prime factors of 75 with the help of the division method is discussed here.

Table of Contents:

• What are the Factors of 75?
• Pair Factors of 75
• How to Find the Prime Factors of 75?
• Prime Factorization of 75
• Examples
• FAQs

What are the Factors of 75?

The factors of 75 are the numbers that are multiplied in pairs resulting in the original number 75. In other words, the factors of 75 are the numbers that divide the number 75 exactly without leaving any remainder. As the number 75 is a composite number, it has many factors other than one and the number itself.  Thus, the factors of 75 are 1, 3, 5, 15, 25 and 75.

Pair Factors of 75

To find the pair factors, multiply the two numbers in a pair to get the original number as 75; such numbers are as follows.

If 1 × 75 = 75, then (1, 75) is a pair factor of 75.

Similarly, let us find another pair.

3 × 25 = 75, (3, 25) is a pair factor of 75

5 × 15 = 75, (5, 15) is a pair factor of 75

25 × 3 = 75, (25, 3) is a pair factor of 75

15 × 5 = 75, (15, 5) is a pair factor of 75

Here,(3, 25) is the same as (25, 3) and (5, 15) is the same as (15, 5)

Therefore, the positive pair factors of 75 are (1, 75), (3, 25), and (5, 15).

To find the negative pair factors, then proceed with the following steps

If -1 × -75 = 75, then (-1,- 75) is a pair factor of 75

-3 × -25 = 75, (-3, -25) is a pair factor of 75

-5 × -15 = 75, (-5, -15) is a pair factor of 75

-25 × -3 = 75, (-25, -3) is a pair factor of 75

-15 × -5 = 75, (-15, -5) is a pair factor of 75

Here,(-3, -25) is the same as (-25, -3) and (-5, -15) is the same as (-15, -5)

Therefore, the negative pair factors of 75 are (-1, -75), (-3, -25), and (-5, – 15).

How to calculate the Prime Factors of 75?

Learn the following steps to calculate the factors of a number.

• First, write the number 75
• Find the two numbers, which give the result as 75 under the multiplication, say 3 and 25, such as 3 × 25 = 75.
• We know that 3 is a prime number that has only two factors, i.e., 1 and the number itself( 1 and 3). So, it cannot be further factorized.
• 3 = 3 × 1

• But look at the number 25, which is a composite number but not a prime number. So it can be further factorized.
• 25 = 5 × 5 × 1

• Therefore, the factorization of 75 is written as 75 = 3 × 5 × 5 × 1
• Finally, write down all the unique numbers (i.e.,) 3 ×  5 × 5 × 1.

Prime Factorization of 75

The number 75 is a composite, and it should have prime factors. Now let us know how to calculate the prime factors.

• • The first step is to divide the number 75 with the smallest prime factor, say 2. If we divide 75/2, we will get a fractional value, and hence proceed with the next prime factor, (i.e.) 3.
  • 75 ÷ 3 = 25
  • Now, if we divide 25 by 3, we will get a fractional number, which cannot be a factor.

• • So, now proceed with the next prime numbers, i.e.

                    25 ÷ 5 = 5

                    5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 75 are written as 3 × 5 × 5 or 3 x 5², where 3 and 5 are the prime numbers.

Video Lesson on Prime Factors

Examples

Example 1:

Find the common factors of 75 and 73.

Solution:

The factors of 75 are 1, 3, 5, 15, 25 and 75. 

The factors of 73 are 1 and 73

Thus, the common factor of 75 and 73 is 1.

Example 2:

Find the common factors of 75 and 76.

Solution:

Factors of 75 = 1, 3, 5, 15, 25 and 75.

Factors of 76 = 1, 2, 4, 19, 38, and 76.

Therefore, the common factor of 75 and 76 is 1.

Example 3:

Find the common factors of 75 and 150.

Solution:

The factors of 75 are 1, 3, 5, 15, 25 and 75.

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

Hence, the common factors of 75 and 150 are 1, 3, 5, 15, 25 and 75.

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