Factors of 963

Factors are numbers that combine through multiplication to give the original number as the result.

For example:
963× 1 = 963
321 × 3 = 963
107 × 9 = 963 … and so on.

Factors of 963 are 1, 3, 9, 107, 321, and 963. These numbers divide 963 without leaving a remainder. Along with positive factors, there will also be corresponding negative factors.

Negative Factors of 963:  -1, -3, -9, -107, -321, -963.
Prime Factors of 963:  3 and 107.
Prime factorization of 963:  32 × 107.
Sum of Factors of 963:  1 + 3 + 9 + 107 + 321 + 963 = 1404.

Identifying the factors of 963 is useful in different scenarios, and it helps to break down the number into smaller and more manageable parts, making it easier to understand. Here are the important methods that you can find the factors of 963:

• Multiplication method
• Division method
• Prime factors and prime factorization method

The multiplication method involves finding the pairs of numbers that multiply together to give the original number. For example: 1 × 963 = 963, so here both 1 and 963 are the factors of 963.

To find all the pairs of numbers that multiply to give 963, here are the steps to follow.

Step 1: All the numbers are divisible by 1 and the number itself, so start with 1 and the number itself,
 1 × 963 = 963 
And the factors are 1 and 963.

Step 2: Now check divisibility by 2, 3, 4, 5, etc.

 Start with smaller numbers 2, 3, and so on. Stop checking once you reach the square root of 963, (which is approximately 31). Any factor larger than the square root of 963 will have a corresponding smaller factor, so checking the divisibility up to 31 is needed.

Check divisibility by 3: To check if 963 is divisible by 3, we need to sum the digits of 963:
9 + 6 + 3 = 18, where 18 is divisible by 3. So, 963 is divisible by 3.
963 ÷ 3 = 321

And the factors are 3 and 321.

Check divisibility by 9: To check if 963 is divisible by 9, we need to sum the digits of 963 again: 9 + 6 + 3 = 18, and 18 is divisible by 9. Now we divide 963 by 9:

963 ÷ 9 = 107 

And the factors are 9 and 107.

Step 3: From the steps we have done above, the factors of pairs of 963 are: 

 1 × 963, 3 × 321, 9 × 107

The factors of 963, which we get through the multiplication method, are:

1, 3, 9, 107, 321, and 963.

The division method involves finding the factors that divide a number by smaller numbers, which ones divide it evenly. If the result is an integer, then both the divisor and the quotient are factors of the number.

Step 1: Divide 963 by 1 – 963 ÷ 1 = 963.
Step 2: Divide 963 by 3 – 963 ÷ 3 = 321.
Step 3: Divide 963 by 9– 963 ÷9 = 107.

The whole step shows that all the numbers divide 963 evenly, and the factors are

1, 3, 9, 107, 321, 963

Prime factors are prime numbers that divide the given number evenly without leaving a remainder.
Prime factorization is a process of expressing numbers into its prime factors that, when multiplied together, give the original number.

Prime Factors of 963: Prime factors of 963 are 3 and 107.

There are 2 common methods to find the prime factors of a number and they are:

• Prime Factorization 
• Factor Tree

Prime Factorization of 963: Prime factorization is the process of expressing numbers to prime factors by breaking them. Here is the step-by-step solution for 963: 

The prime factorization of 963 is: 

963 = 3  x 3  x107 or 3² x  107

A factor tree visually depicts how a number breaks down into its prime factors. This process involves step-by-step, beginning with the smallest prime number and continuing until only prime factors remain, as shown below.

Step 1: Start with 963:

 Select two factors of 963, which is 3 and 321.

Step 2: Factors of 321:

321 = 3 × 107

Step 3: Now check 107:

107 is a prime number, so it cannot be factored further.

Factor pairs are two numbers that, when multiplied together, produce the original number. Each pair includes one number that divides the original number evenly and the resulting quotient.

Positive pair factors: (1, 963), (3, 321), (9, 107)
Negative pair factors: (−1, −963), (−3, −321), (−9, −107)

• Factor Tree: A factor tree graphically represents how numbers are broken down into fewer factors. 

•  Factor pair: A pair of numbers, when multiplied together, bring the original number. Each pair includes two numbers that divide the original number evenly, leaving no remainder. For example: Number 6 - factor pairs: (1, 6), (2, 3).

•  Composite number: It is an integer greater than 1 and has more than two factors. For example 15: Divisors - 1, 3, 5, 15: factor pairs: (1, 15), (3, 5).

• Multiple: A multiple of a number is the result of multiplying a number by an integer. Example: 1926 is a multiple of 963 because 963 × 2 = 1926.

•  Prime factorization: Prime factorization is a process of breaking numbers into their factor. These prime factors result in the original number when they are multiplied.