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Factors of 957: Prime Factorization, Methods, and Examples

The factors of 957 are numbers that, when divided by 957, leave zero as the remainder. This means the numbers that ultimately divide the given number are named as their factors.

 The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 957

Here are the factors of number 957.

Factors of 957: 1, 3, 11, 29, 33, 87, 319, and 957 

Negative Factors of 957

The negative factors of 957 are similar to their positive aspects, just with a negative sign.

Negative Factors of 957: –1, -3, -11, -29, -33, -87, -319, and -957 

Prime Factorization of 957

The prime factorization of 957 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 11 x 29

In this article, we will learn about the factors of 957 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 957?

The factors of 957 are 1, 3, 11, 29, 33, 87, 319, and 957. These numbers are the factors as they do not leave any remainder when divided by 957.

The factors of 957 are classified as prime numbers and composite numbers. The prime factors of the number 957 can be determined using the prime factorization technique.

How To Find the Factors of 957?

You can find the factors of 957 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 957, create a list containing the numbers that are exactly divisible by 957 with zero remainders. One important thing to note is that 1 and 957 are 957’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 957 are determined as follows:

\[\dfrac{957}{1} = 957\]

\[\dfrac{957}{3} = 319\]

\[\dfrac{957}{11} = 87\]

\[\dfrac{957}{29} = 33\]

Therefore, 1, 3, 11, 29, 33, 87, 319, and 957 are the factors of 957.

Total Number of Factors of 957

For 957, there are eight positive factors and eight negative ones. So in total, there are sixteen factors of 957. 

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 957 is given as:

The factorization of 957 is 1 x 3 x 11 x 29.

The exponent of 1, 3, 11, and 29 is 1.

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

Therefore, the total number of factors of 957 is 16. Eight are positive, and eight 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 957 by Prime Factorization

The number 957 is a composite. 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 957 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 957, 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 957 can be expressed as:

957 = 3 x 11 x 29

Factors of 957 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 957, the factor pairs can be found as:

1 x 957 = 957

3 x 319 = 957

11 x 87 = 957

29 x 33 = 957 

The possible factor pairs of 957 are given as (1, 957), (3, 319), (11, 87), and (29, 33).

All these numbers in pairs, when multiplied, give 957 as the product.

The negative factor pairs of 957 are given as:

-1 x -957 = 957

-3 x -319 = 957

-11 x -87 = 957

-29 x -33 = 957 

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, -11, -29, -33, -87, -319, and -957 are called negative factors of 957.

The list of all the factors of 957, including positive as well as negative numbers, is given below.

Factor list of 957: 1, -1, 3, -3, 11, -11, 29, -29, 33, -33, 87, -87, 319, -319, 957, and -957 

Factors of 957 Solved Examples

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

Example 1

How many factors of 957 are there?

Solution

The total number of Factors of 957 is eight.

Factors of 957 are 1, 3, 11, 29, 33, 87, 319, and 957.

Example 2

Find the factors of 957 using prime factorization.

Solution

The prime factorization of 957 is given as:

957 $\div$ 3 = 319

319 $\div$ 11 = 29 

29 $\div$ 29 = 1 

So the prime factorization of 957 can be written as:

2 x 11 x 29 = 957

Factors of 956|Factors List| Factors of 958

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