Factors of 961: Prime Factorization, Methods, and Examples

 The number 961 when used as a dividend then the only divisor which gives the whole number is 31 we said this number is even as well as a composite. 

Factors Of 961

As far as 961 is concerned it is a perfect square number.

Factors of 961

Here are the factors of number 961.

Factors of 961: 1, 31, and 961

Negative Factors of 961

The negative factors of 961 are similar to its positive aspects, just with a negative sign.

Negative Factors of 961: -1, -31, and -961

Prime Factorization of 961

The prime factorization of 961 is the way of expressing its prime factors in the product form.

Prime Factorization: 31 x 31

In this article, we will learn about the factors of 961 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 961?

The factors of 961 are 1, 31, and 961. These numbers are the factors as they do not leave any remainder when divided by 961.

The factors of 961 are classified as prime numbers and composite numbers. The prime factors of the number 961 can be determined using the prime factorization technique.

How To Find the Factors of 961?

You can find the factors of 961 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 961, create a list containing the numbers that are exactly divisible by 961 with zero remainders. One important thing to note is that 1 and 961 are the 961’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 961 are determined as follows:

\[\dfrac{961}{1} = 961\]

\[\dfrac{961}{31} = 31\]

\[\dfrac{961}{961} = 1\]

Therefore, 1, 31, and 961 are the factors of 961.

Total Number of Factors of 961

For 961, there are 3 positive factors and 3 negative ones. So in total, there are 6 factors of 961.

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 961 is given as:

Factorization of 961 is 31 x 31.

The exponent of 31 and 31 is 2.

Adding 1 to each and multiplying them together results in 3.

Therefore, the total number of factors of 961 is six. Three are positive, and three 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 961 by Prime FactorizationFactor of 961 by Prime Factorization

The number 961 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 961 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 961, 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 961 can be expressed as:

961 = 31 x 31

Factors of 961 in PairsFactor of 961 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 961, the factor pairs can be found as:

1 x 961 = 961

31 x 31 = 961

The possible factor pairs of 961 are given as (1, 961) and (31, 31).

All these numbers in pairs, when multiplied, give 961 as the product.

The negative factor pairs of 961 are given as:

-1 x -961 = 961

-31 x -31 = 961

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, -31, and -961 are called negative factors of 961.

The list of all the factors of 961, including positive as well as negative numbers, is given below.

Factor list of 961: 1, -1, 31, -31, 961, and -961

Factors of 961 Solved Examples

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

Example 1

How many factors of 961 are there?


The total number of Factors of 961 is three.

Factors of 961 are 1, 31, and 961.

Example 2

Find the factors of 961 using prime factorization.


The prime factorization of 961 is given as:

961 $\div$ 31 = 31 

31 $\div$ 31 = 1 

So the prime factorization of 961 can be written as:

31 x 31 = 961

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