Hi Students, welcome to **Amans Maths Blogs (AMB)**. Do you want to learn how to * Find All Factors of 75 | Prime Factorization of 75 | Multiples of 75 *? Then, read this article.

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## Definition of Factors of 75 in Math

If you divide 75 by a number and, when it gives remainder as zero, then the number is called the factor of 75 or the divisors of 75. The factors of 75 are the natural numbers. The factors of 75 cannot be decimals or fractions.

## What are the factors of 75?

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

## How to find Factors of 75

Finding the factors of 68 is finding the exactly divisors of 75. For this, you need to divide 75 by every natural number up to 75, which leaves remainder zero. You must remember that 1 is a factor of every number and the number itself is a factor.

75 ÷ 1 = 75, so 1 is a factor of 75.

75 ÷ 2 = Decimal Number, so 2 is not a factor of 75.

75 ÷ 3 = 25, so 3 is a factor of 75.

75 ÷ 4 = Decimal Number, so 4 is not a factor of 75.

75 ÷ 5 = 15, so 5 is a factor of 75.

75 ÷ 6 = Decimal Number, so 6 is not a factor of 75.

75 is divided by 7, 8, 9 …14, gives a decimal numbers, these are not factors of 75.

75 ÷ 15 = 5, so 15 is a factor of 75.

75 ÷ 16 = Decimal Number, so 16 is not a factor of 75.

75 is divided by 17, 18, 19, 20, … 24, gives a decimal numbers, these are not factors of 75.

75 ÷ 25 = 3, so 25 is a factor of 75.

75 ÷ 26 = Decimal Number, so 26 is not a factor of 75.

75 is divided by 27, 28, 29 … 74, gives a decimal numbers, these are not factors of 75.

75 ÷ 75 = 1, so 75 is a factor of 75.

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

## How many factors of 75?

On counting the number of factors of 75, you get that there are 6 factors of 75.

## Multiples of 75

The multiples of a number is infinite. Thus, first 10 multiples of 75 are 75, 150, 225, 300, 375, 450, 525, 625, 675, 750.

## Difference between factors and multiples

The factor of a number does leave any remainder when the number is divided by its factor, whereas the multiple of a number is a number which is obtained by multiplying with another number.

The number of factors of a number is finite, whereas the multiples of a number is infinite.

## Why 68 is not a prime number?

A prime number has only two factors, 1 and itself. But, the number of factors of 75 are more than two. Thus, 75 is not a prime number.

## Prime Factorization of 75

The prime factorization of 75 is the list of prime numbers whose product is 75. A prime factorization of 75 is unique to represent the product of prime factors of 75. There is exactly one prime factorization for any given number.

The prime factorization of 75 is 75 = 3 × 5^{2}.

## How to calculate Prime Factorization of 75

To determine a prime factorization of a number, start with a list of known primes and then divide them repeatedly into the quotients. Continue this process until you get 1. Thus, to find the prime factorization of 75, you need to divide 75 by each of prime number up to 75.

Step 1: 75 is not divisible by 2, you need to divided 75 by next prime factors of 75 that is 3.

75 ÷ 3 = 25

Step 2: Now, 25 is not divisible by 3, you need to divided 25 by next prime factors of 75 that is 5.

25 ÷ 5 = 5

Step 3:

5 ÷ 5 = 1

Now, you get the quotient 1 then stop. Thus, the prime factorization of 75 is

75 = 3 × 5 × 5 = 3 × 5^{2}.

## Factors Pairs of 75

The pairs of factors of 75 whose the product is 75 are the factors pairs of 75.

1 × 75 = 75

3 × 25 = 75

5 × 15 = 75

Thus, the factors pairs of 75 are

(1 and 75),

(3 and 25),

(5 and 15),

## List of Positive Factors of 75

The factors of 75 can be positive or negative.

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

## List of Negative Factors of 75

The factors of 75 can be positive or negative.

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

## Prime Factors of 68

A prime number is a number, which is divisible by 1 and itself.

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

In the factors of 75, Since 2 and 5 are prime numbers, then the prime factors of 75 are 3 and 5 only.

## How many prime factors of 75?

There are two prime factors of 75, that are 3 and 5.

Formula for Total Factors | Formula for Even Factors |

Formula for Odd Factors | Formula for Sum of All Factors |

Formula for Product of All Factors | Factors & Multiples |