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Factors of 975: Prime Factorization, Methods, and Examples

The numbers that produce zero as the remainder when 975 is used as their dividend are known as the factors of 975. 

Given that the given number is obtained by multiplying integers with two factors, its factors may be both positive and negative.

Factors of 975

Here are the factors of number 975.

Factors of 975: 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975

Negative Factors of 975

The negative factors of 975 are similar to their positive aspects, just with a negative sign.

Negative Factors of 975: -1, -3, -5, -13, -15, -25, -39, -65, -75, -195, -325, and -975

Prime Factorization of 975

The prime factorization of 975 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 5 x 5 x 13 

In this article, we will learn about the factors of 975 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 975?

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975. These numbers are the factors as they do not leave any remainder when divided by 975.

The factors of 975 are classified as prime numbers and composite numbers. The prime factors of the number 975 can be determined using the prime factorization technique.

How To Find the Factors of 975?

You can find the factors of 975 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 975, create a list containing the numbers that are exactly divisible by 975 with zero remainders. One important thing to note is that 1 and 975 are the 975’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 975 are determined as follows:

\[\dfrac{975}{1} = 975\]

\[\dfrac{975}{3} = 325\]

\[\dfrac{975}{5} = 195\]

\[\dfrac{975}{13} = 75\]

\[\dfrac{975}{15} = 65\]

\[\dfrac{975}{25} = 39\]

\[\dfrac{975}{39} = 25\]

\[\dfrac{975}{65} = 15\]

\[\dfrac{975}{75} = 13\]

\[\dfrac{975}{195} = 5\]

\[\dfrac{975}{325} = 3\]

\[\dfrac{975}{975} = 1\]

Therefore, 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975 are the factors of 975.

Total Number of Factors of 975

For 975, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors out of 975. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of 975 is given as:

Factorization of 975 is 3 x 5 x 5 x 13 .

The exponent of 3 is 1, 5 is 2, and 13 is 1.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 975 is 24. 12 are positive, and 12 factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 975 by Prime Factorization

The number 975 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 975 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 975, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 975 can be expressed as:

975 = 3 x 5 x 5 x 13 

Factors of 975 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 975, the factor pairs can be found as:

1 x 975 = 975

3 x 325 = 975

5 x 195 = 975

13 x 75 = 975

15 x 65 = 975

25 x 39 = 975

The possible factor pairs of 975 are given as (1, 975)(3, 325 )(5, 195 )(13, 75 )(15, 65 ), and (25, 39 ).

All these numbers in pairs, when multiplied, give 975 as the product.

The negative factor pairs of 975 are given as:

-1 x -975 = 975

-3 x -325 = 975

-5 x -195 = 975

-13 x -75 = 975

-15 x -65 = 975

-25 x -39 = 975

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1, -3, -5, -13, -15, -25, -39, -65, -75, -195, -325, and -975 are called negative factors of 975.

The list of all the factors of 975, including positive as well as negative numbers, is given below.

Factor list of 975: 1,-1, 3,-3, 5,-5, 13,-13, 15,-15, 25,-25, 39,-39, 65,-65, 75,-75, 195,-195, 325,-325, 975, and -975

Factors of 975 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 975 are there?

Solution

The total number of Factors of 975 is 24.

Factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975.

Example 2

Find the factors of 975 using prime factorization.

Solution

The prime factorization of 975 is given as:

975 $\div$ 3 = 325 

325 $\div$ 5 = 65 

65 $\div$ 5 = 13 

13 $\div$ 13 = 1 

So the prime factorization of 975 can be written as:

3 x 5 x 5 x 13  =975

Factors of 974|Factors List| Factors of 976

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