Factors of 1176

The numbers that divide 1176 evenly are known as factors of 1176. A factor of 1176 is a number that divides the number without remainder. The factors of 1176 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, and 1176.

Negative factors of 1176: -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -42, -49, -56, -84, -98, -147, -168, -196, -294, -392, -588, and -1176.

Prime factors of 1176: 2, 3, and 7.

Prime factorization of 1176: 2³ × 3 × 7².

The sum of factors of 1176: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 42 + 49 + 56 + 84 + 98 + 147 + 168 + 196 + 294 + 392 + 588 + 1176 = 4032

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 1176. Identifying the numbers which are multiplied to get the number 1176 is the multiplication method.

Step 1: Multiply 1176 by 1, 1176 × 1 = 1176.

Step 2: Check for other numbers that give 1176 after multiplying

2 × 588 = 1176

3 × 392 = 1176

4 × 294 = 1176

6 × 196 = 1176

7 × 168 = 1176

8 × 147 = 1176

12 × 98 = 1176

14 × 84 = 1176

16 × 73.5 = not a factor

21 × 56 = 1176

28 × 42 = 1176

Therefore, the positive factor pairs of 1176 are: (1, 1176), (2, 588), (3, 392), (4, 294), (6, 196), (7, 168), (8, 147), (12, 98), (14, 84), (21, 56), (28, 42). All these factor pairs result in 1176. 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 1176 by 1, 1176 ÷ 1 = 1176.

Step 2: Continue dividing 1176 by the numbers until the remainder becomes 0.

1176 ÷ 1 = 1176

1176 ÷ 2 = 588

1176 ÷ 3 = 392

1176 ÷ 4 = 294

1176 ÷ 6 = 196

1176 ÷ 7 = 168

1176 ÷ 8 = 147

1176 ÷ 12 = 98

1176 ÷ 14 = 84

1176 ÷ 21 = 56

1176 ÷ 28 = 42

Therefore, the factors of 1176 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, and 1176.

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 1176 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1176 ÷ 2 = 588

588 ÷ 2 = 294

294 ÷ 2 = 147

147 ÷ 3 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

The prime factors of 1176 are 2, 3, and 7. The prime factorization of 1176 is: 2³ × 3 × 7².

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

Step 1: Firstly, 1176 is divided by 2 to get 588.

Step 2: Now divide 588 by 2 to get 294.

Step 3: Then divide 294 by 2 to get 147.

Step 4: Divide 147 by 3 to get 49.

Step 5: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1176 is: 2³ × 3 × 7².

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 1176: (1, 1176), (2, 588), (3, 392), (4, 294), (6, 196), (7, 168), (8, 147), (12, 98), (14, 84), (21, 56), (28, 42).
• Negative factor pairs of 1176: (-1, -1176), (-2, -588), (-3, -392), (-4, -294), (-6, -196), (-7, -168), (-8, -147), (-12, -98), (-14, -84), (-21, -56), (-28, -42).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1176 are 1, 2, 3, 4, 6, 7, etc.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 1176.

• 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 1176 are (1, 1176), (2, 588), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1176 is 2³ × 3 × 7².

• Negative factors: The negative counterparts of positive factors. For example, the negative factors of 1176 include -1, -2, -3, etc.