Factors of 966

The numbers that divide 966 evenly are known as factors of 966.

A factor of 966 is a number that divides the number without remainder.

The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 29, 42, 46, 58, 69, 87, 138, 161, 203, 322, 483, and 966.

Negative factors of 966: -1, -2, -3, -6, -7, -14, -21, -23, -29, -42, -46, -58, -69, -87, -138, -161, -203, -322, -483, and -966.

Prime factors of 966: 2, 3, 7, and 23.

Prime factorization of 966: 2 × 3 × 7 × 23.

The sum of factors of 966: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 29 + 42 + 46 + 58 + 69 + 87 + 138 + 161 + 203 + 322 + 483 + 966 = 2660

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
  
   
• Finding factors using division method
  
   
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 966. Identifying the numbers which are multiplied to get the number 966 is the multiplication method.

Step 1: Multiply 966 by 1, 966 × 1 = 966.

Step 2: Check for other numbers that give 966 after multiplying

2 × 483 = 966

3 × 322 = 966

6 × 161 = 966

7 × 138 = 966

14 × 69 = 966

21 × 46 = 966

23 × 42 = 966

29 × 33 = 966

Therefore, the positive factor pairs of 966 are: (1, 966), (2, 483), (3, 322), (6, 161), (7, 138), (14, 69), (21, 46), (23, 42), and (29, 33).

For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 966 by 1, 966 ÷ 1 = 966.

Step 2: Continue dividing 966 by the numbers until the remainder becomes 0.

966 ÷ 1 = 966

966 ÷ 2 = 483

966 ÷ 3 = 322

966 ÷ 6 = 161

966 ÷ 7 = 138

966 ÷ 14 = 69

966 ÷ 21 = 46

966 ÷ 23 = 42

966 ÷ 29 = 33

Therefore, the factors of 966 are: 1, 2, 3, 6, 7, 14, 21, 23, 29, 33, 42, 46, 69, 138, 161, 322, 483, 966.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

Using prime factorization

Using factor tree

Using Prime Factorization: In this process, prime factors of 966 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

966 ÷ 2 = 483

483 ÷ 3 = 161

161 ÷ 7 = 23

23 ÷ 23 = 1

The prime factors of 966 are 2, 3, 7, and 23. The prime factorization of 966 is: 2 × 3 × 7 × 23.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 966 is divided by 2 to get 483.

Step 2: Now divide 483 by 3 to get 161.

Step 3: Then divide 161 by 7 to get 23.

Here, 23 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 966 is: 2 × 3 × 7 × 23.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Both positive and negative factors constitute factor pairs.

Positive factor pairs of 966: (1, 966), (2, 483), (3, 322), (6, 161), (7, 138), (14, 69), (21, 46), (23, 42), (29, 33).

Negative factor pairs of 966: (-1, -966), (-2, -483), (-3, -322), (-6, -161), (-7, -138), (-14, -69), (-21, -46), (-23, -42), (-29, -33).

• Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 966 are 1, 2, 3, etc.
  
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 23 are prime factors of 966.
  
   
• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 966 are (1, 966), (2, 483), etc.
  
   
• Prime factorization: The expression of a number as the product of its prime factors. For example, 966 = 2 × 3 × 7 × 23.
  
   
• Multiple: A number that can be divided by another number without a remainder. For example, 966 is a multiple of 3.