Factors of 1152

The numbers that divide 1152 evenly are known as factors of 1152. A factor of 1152 is a number that divides the number without remainder. The factors of 1152 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152.

Negative factors of 1152: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -48, -64, -72, -96, -128, -144, -192, -288, -384, -576, and -1152.

Prime factors of 1152: 2 and 3.

Prime factorization of 1152: 2⁷ × 3².

The sum of factors of 1152: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 48 + 64 + 72 + 96 + 128 + 144 + 192 + 288 + 384 + 576 + 1152 = 3367

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 1152. Identifying the numbers which are multiplied to get the number 1152 is the multiplication method.

Step 1: Multiply 1152 by 1, 1152 × 1 = 1152.

Step 2: Check for other numbers that give 1152 after multiplying

2 × 576 = 1152

3 × 384 = 1152

4 × 288 = 1152

6 × 192 = 1152

8 × 144 = 1152

9 × 128 = 1152

12 × 96 = 1152

16 × 72 = 1152

18 × 64 = 1152

24 × 48 = 1152

32 × 36 = 1152

Therefore, the positive factor pairs of 1152 are: (1, 1152), (2, 576), (3, 384), (4, 288), (6, 192), (8, 144), (9, 128), (12, 96), (16, 72), (18, 64), (24, 48), (32, 36). 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 1152 by 1, 1152 ÷ 1 = 1152.

Step 2: Continue dividing 1152 by the numbers until the remainder becomes 0.

1152 ÷ 1 = 1152

1152 ÷ 2 = 576

1152 ÷ 3 = 384

1152 ÷ 4 = 288

1152 ÷ 6 = 192

1152 ÷ 8 = 144

1152 ÷ 9 = 128

1152 ÷ 12 = 96

1152 ÷ 16 = 72

1152 ÷ 18 = 64

1152 ÷ 24 = 48

1152 ÷ 32 = 36

Therefore, the factors of 1152 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, and 1152.

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 1152 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1152 ÷ 2 = 576

576 ÷ 2 = 288

288 ÷ 2 = 144

144 ÷ 2 = 72

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of 1152 are 2 and 3. The prime factorization of 1152 is: 2⁷ × 3².

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

Step 1: Firstly, 1152 is divided by 2 to get 576.

Step 2: Now divide 576 by 2 to get 288.

Step 3: Then divide 288 by 2 to get 144.

Step 4: Divide 144 by 2 to get 72.

Step 5: Divide 72 by 2 to get 36. Step 6: Divide 36 by 2 to get 18.

Step 7: Divide 18 by 2 to get 9.

Step 8: Divide 9 by 3 to get 3.

Step 9: Divide 3 by 3 to get 1. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1152 is: 2⁷ × 3².

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 1152: (1, 1152), (2, 576), (3, 384), (4, 288), (6, 192), (8, 144), (9, 128), (12, 96), (16, 72), (18, 64), (24, 48), and (32, 36).
• Negative factor pairs of 1152: (-1, -1152), (-2, -576), (-3, -384), (-4, -288), (-6, -192), (-8, -144), (-9, -128), (-12, -96), (-16, -72), (-18, -64), (-24, -48), and (-32, -36).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1152 are 1, 2, 3, etc.

• Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 1152.

• 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 1152 are (1, 1152), (2, 576), etc.

• Prime factorization: The expression of a number as a product of its prime numbers. For example, the prime factorization of 1152 is 2⁷ × 3².

• Sum of factors: The total sum when all factors of a number are added together. For example, the sum of factors of 1152 is 3367.