Factors of 924

The numbers that divide 924 evenly are known as factors of 924. A factor of 924 is a number that divides the number without remainder. The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.

Negative factors of 924: -1, -2, -3, -4, -6, -7, -11, -12, -14, -21, -22, -28, -33, -42, -44, -66, -77, -84, -132, -154, -231, -308, -462, and -924.

Prime factors of 924: 2, 3, 7, and 11.

Prime factorization of 924: 2 × 2 × 3 × 7 × 11.

The sum of factors of 924: 1 + 2 + 3 + 4 + 6 + 7 + 11 + 12 + 14 + 21 + 22 + 28 + 33 + 42 + 44 + 66 + 77 + 84 + 132 + 154 + 231 + 308 + 462 + 924 = 2520

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

1. Finding factors using multiplication
2. Finding factors using the division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 924. Identifying the numbers which are multiplied to get the number 924 is the multiplication method.

Step 1: Multiply 924 by 1, 924 × 1 = 924.

Step 2: Check for other numbers that give 924 after multiplying

2 × 462 = 924

3 × 308 = 924

4 × 231 = 924

6 × 154 = 924

7 × 132 = 924

11 × 84 = 924

12 × 77 = 924

14 × 66 = 924

21 × 44 = 924

22 × 42 = 924

28 × 33 = 924

Therefore, the positive factor pairs of 924 are: (1, 924), (2, 462), (3, 308), (4, 231), (6, 154), (7, 132), (11, 84), (12, 77), (14, 66), (21, 44), (22, 42), and (28, 33). For every positive factor, there is a negative factor.

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

Step 1: Divide 924 by 1, 924 ÷ 1 = 924.

Step 2: Continue dividing 924 by the numbers until the remainder becomes 0.

924 ÷ 1 = 924

924 ÷ 2 = 462

924 ÷ 3 = 308

924 ÷ 4 = 231

924 ÷ 6 = 154

924 ÷ 7 = 132

924 ÷ 11 = 84

924 ÷ 12 = 77

924 ÷ 14 = 66

924 ÷ 21 = 44

924 ÷ 22 = 42

924 ÷ 28 = 33

Therefore, the factors of 924 are: 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924.

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 924 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

924 ÷ 2 = 462

462 ÷ 2 = 231

231 ÷ 3 = 77

77 ÷ 7 = 11

11 ÷ 11 = 1

The prime factors of 924 are 2, 3, 7, and 11. The prime factorization of 924 is: 2 × 2 × 3 × 7 × 11.

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

Step 1: Firstly, 924 is divided by 2 to get 462.

Step 2: Now divide 462 by 2 to get 231.

Step 3: Then divide 231 by 3 to get 77.

Step 4: Divide 77 by 7 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 924 is: 2 × 2 × 3 × 7 × 11.

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 924: (1, 924), (2, 462), (3, 308), (4, 231), (6, 154), (7, 132), (11, 84), (12, 77), (14, 66), (21, 44), (22, 42), (28, 33).

• Negative factor pairs of 924: (-1, -924), (-2, -462), (-3, -308), (-4, -231), (-6, -154), (-7, -132), (-11, -84), (-12, -77), (-14, -66), (-21, -44), (-22, -42), (-28, -33).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, and 924.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 11 are prime factors of 924.

• 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 924 are (1, 924), (2, 462), etc.

• Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 924 is 2 × 2 × 3 × 7 × 11.

• Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number. For example, finding that 2 × 462 = 924.