1. Steps to find factors of 963 using Division Method

Example: Find factors of 963

  • Divide 963 by 1: 963 ÷ 1 : Remainder = 0
  • Divide 963 by 3: 963 ÷ 3 : Remainder = 0
  • Divide 963 by 9: 963 ÷ 9 : Remainder = 0
  • Divide 963 by 107: 963 ÷ 107 : Remainder = 0
  • Divide 963 by 321: 963 ÷ 321 : Remainder = 0
  • Divide 963 by 963: 963 ÷ 963 : Remainder = 0

Hence, Factors of 963 are 1, 3, 9, 107, 321, and 963

2. Steps to find factors of 963 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 963 using the division method, follow these steps:

  • Step 1. Start dividing 963 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 963, which is 3. Divide 963 by 3 to obtain the quotient (321).
    963 ÷ 3 = 321
  • Step 3. Repeat step 1 with the obtained quotient (321).
    321 ÷ 3 = 107
    107 ÷ 107 = 1

So, the prime factorization of 963 is, 963 = 3 x 3 x 107.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 963 as shown below:

So, the prime factorization of 963 is, 963 = 3 x 3 x 107.

3. Find factors of 963 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 963 would be the two numbers which, when multiplied, give 963 as the result.

The following table represents the calculation of factors of 963 in pairs:

Factor Pair Pair Factorization
1 and 963 1 x 963 = 963
3 and 321 3 x 321 = 963
9 and 107 9 x 107 = 963

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 963. They are called negative pair factors.

Hence, the negative pairs of 963 would be ( -1 , -963 ) , ( -3 , -321 ) and ( -9 , -107 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Every number is a factor of zero (0), since 963 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 3, 9, 107, 321, 963 are exact divisors of 963.
  • Factors of 963 are 1, 3, 9, 107, 321, 963. Each factor divides 963 without leaving a remainder.

Frequently Asked Questions

  • Which is the smallest prime factor of 963?

    Smallest prime factor of 963 is 3.

  • Is 963 a perfect square?

    No 963 is not a perfect square.

  • What are five multiples of 963?

    First five multiples of 963 are 1926, 2889, 3852, 4815, 5778.

  • What is prime factorization of 963?

    Prime factorization of 963 is 3 x 3 x 107.

  • What are factors of 963?

    Factors of 963 are 1, 3, 9, 107, 321, 963.

  • How do you find factors of a negative number? ( eg. -963 )?

    Factors of -963 are -1, -3, -9, -107, -321, -963.

  • Is 963 a whole number?

    Yes 963 is a whole number.

  • Which is greatest factor of 963?

    The greatest factor of 963 is 321.

  • What are the prime factors of 963?

    The factors of 963 are 1, 3, 9, 107, 321, 963.
    Prime factors of 963 are 3, 3, 107.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 963. Can you help her?

Prime factors of 963 are 3, 3, 107.
Hence, the product of prime factors of 321.

Can you help Rubel to find out the product of the even factors of 963?

Factors of 963 are 1, 3, 9, 107, 321, 963.
Even factors of 963 are 0.
Hence, product of even factors of 963 is; 0 = 0.

Joy wants to calculate mean of all the factors of 963. Help him in finding the mean of 963.

Factors of 963 are 1, 3, 9, 107, 321, 963.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 963 is 1 + 3 + 9 + 107 + 321 + 963 = 1404.
Hence, the mean of factors of 963 is 1404 ÷ 6 = 234.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 963? Help her in writing all the factors.

Positive factors are 1, 3, 9, 107, 321, 963.
Negative factors are -1, -3, -9, -107, -321, -963.

How many factors are there for 963?

Factors of 963 are 1, 3, 9, 107, 321, 963.
So there are in total 6 factors.

Joey wants to write all the prime factors of 963 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 963 are 3, 3, 107.
So in exponential form it can be written as 32 x 107.

Kevin has been asked to write 5 factor(s) of 963. Can you predict the answer?

5 factor(s) of 963 are 1, 3, 9, 107, 321.