Factors of 928

The numbers that divide 928 evenly are known as factors of 928. A factor of 928 is a number that divides the number without a remainder. The factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, and 928.

Negative factors of 928: -1, -2, -4, -8, -16, -29, -32, -58, -116, -232, -464, and -928.

Prime factors of 928: 2 and 29.

Prime factorization of 928: 2⁴ × 29.

The sum of factors of 928: 1 + 2 + 4 + 8 + 16 + 29 + 32 + 58 + 116 + 232 + 464 + 928 = 1890

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 928. Identifying the numbers which are multiplied to get the number 928 is the multiplication method.

Step 1: Multiply 928 by 1, 928 × 1 = 928.

Step 2: Check for other numbers that give 928 after multiplying

2 × 464 = 928

4 × 232 = 928

8 × 116 = 928

16 × 58 = 928

29 × 32 = 928

Therefore, the positive factor pairs of 928 are: (1, 928), (2, 464), (4, 232), (8, 116), (16, 58), (29, 32). All these factor pairs result in 928. 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 as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 928 by 1, 928 ÷ 1 = 928.

Step 2: Continue dividing 928 by the numbers until the remainder becomes 0.

928 ÷ 1 = 928

928 ÷ 2 = 464

928 ÷ 4 = 232

928 ÷ 8 = 116

928 ÷ 16 = 58

928 ÷ 29 = 32

Therefore, the factors of 928 are: 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928.

The factors can be found by dividing them 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 928 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

928 ÷ 2 = 464

464 ÷ 2 = 232

232 ÷ 2 = 116

116 ÷ 2 = 58

58 ÷ 2 = 29

29 ÷ 29 = 1

The prime factors of 928 are 2 and 29. The prime factorization of 928 is: 2⁴ × 29.

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

Step 1: Firstly, 928 is divided by 2 to get 464.

Step 2: Now divide 464 by 2 to get 232.

Step 3: Then divide 232 by 2 to get 116.

Step 4: Divide 116 by 2 to get 58.

Step 5: Divide 58 by 2 to get 29. Here, 29 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 928 is: 2⁴ × 29.

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 928: (1, 928), (2, 464), (4, 232), (8, 116), (16, 58), (29, 32).

• Negative factor pairs of 928: (-1, -928), (-2, -464), (-4, -232), (-8, -116), (-16, -58), (-29, -32).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, and 928.

• Prime factors: The factors which are prime numbers. For example, 2 and 29 are prime factors of 928.

• 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 928 are (1, 928), (2, 464), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 928 is 2⁴ × 29.

• Negative factors: These are negative numbers that divide the original number without a remainder. For example, the negative factors of 928 include -1, -2, -4, etc.