Factors of 896

The numbers that divide 896 evenly are known as factors of 896. A factor of 896 is a number that divides the number without a remainder. The factors of 896 are 1, 2, 4, 8, 16, 28, 32, 56, 112, 224, 448, and 896.

Negative factors of 896: -1, -2, -4, -8, -16, -28, -32, -56, -112, -224, -448, and -896.

Prime factors of 896: 2 and 7.

Prime factorization of 896: 2⁷ × 7.

The sum of factors of 896: 1 + 2 + 4 + 8 + 16 + 28 + 32 + 56 + 112 + 224 + 448 + 896 = 1827

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

1. Finding factors using multiplication
2. Finding factors using 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 896. Identifying the numbers which are multiplied to get the number 896 is the multiplication method.

Step 1: Multiply 896 by 1, 896 × 1 = 896.

Step 2: Check for other numbers that give 896 after multiplying

2 × 448 = 896

4 × 224 = 896

8 × 112 = 896

16 × 56 = 896

28 × 32 = 896

Therefore, the positive factor pairs of 896 are: (1, 896), (2, 448), (4, 224), (8, 112), (16, 56), and (28, 32). 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 896 by 1, 896 ÷ 1 = 896.

Step 2: Continue dividing 896 by the numbers until the remainder becomes 0.

896 ÷ 1 = 896

896 ÷ 2 = 448

896 ÷ 4 = 224

896 ÷ 8 = 112

896 ÷ 16 = 56

896 ÷ 28 = 32

Therefore, the factors of 896 are: 1, 2, 4, 8, 16, 28, 32, 56, 112, 224, 448, 896.

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

896 ÷ 2 = 448

448 ÷ 2 = 224

224 ÷ 2 = 112

112 ÷ 2 = 56

56 ÷ 2 = 28

28 ÷ 2 = 14

14 ÷ 2 = 7

7 ÷ 7 = 1

The prime factors of 896 are 2 and 7. The prime factorization of 896 is: 2⁷ × 7.

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

Step 1: Firstly, 896 is divided by 2 to get 448.

Step 2: Now divide 448 by 2 to get 224.

Step 3: Then divide 224 by 2 to get 112.

Step 4: Divide 112 by 2 to get 56.

Step 5: Divide 56 by 2 to get 28.

Step 6: Divide 28 by 2 to get 14.

Step 7: Finally, divide 14 by 2 to get 7.

Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 896 is: 2⁷ × 7.

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 896: (1, 896), (2, 448), (4, 224), (8, 112), (16, 56), (28, 32).
• Negative factor pairs of 896: (-1, -896), (-2, -448), (-4, -224), (-8, -112), (-16, -56), (-28, -32).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 896 are 1, 2, 4, 8, 16, 28, 32, 56, 112, 224, 448, and 896.

• Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 896.

• 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 896 are (1, 896), (2, 448), etc.

• Prime factorization: Breaking down a number into a product of prime factors. For example, the prime factorization of 896 is 2⁷ × 7.

• Multiplication method: A method for finding factors by identifying pairs of numbers that multiply to the given number. For example, finding factor pairs of 896 through multiplication.