Factors of 756

The numbers that divide 756 evenly are known as factors of 756.

A factor of 756 is a number that divides the number without remainder.

The factors of 756 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 28, 36, 54, 84, 108, 189, 252, 378, and 756.

Negative factors of 756: -1, -2, -3, -4, -6, -9, -12, -18, -27, -28, -36, -54, -84, -108, -189, -252, -378, and -756.

Prime factors of 756: 2, 3, and 7.

Prime factorization of 756: 2² × 3³ × 7.

The sum of factors of 756: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 28 + 36 + 54 + 84 + 108 + 189 + 252 + 378 + 756 = 2340

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

• Finding factors using multiplication
   
• Finding factors using division method
   
• Prime factors and prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 756. Identifying the numbers which are multiplied to get the number 756 is the multiplication method.

Step 1: Multiply 756 by 1, 756 × 1 = 756.

Step 2: Check for other numbers that give 756 after multiplying

2 × 378 = 756

3 × 252 = 756

4 × 189 = 756

6 × 126 = 756

9 × 84 = 756

12 × 63 = 756

18 × 42 = 756

27 × 28 = 756

Therefore, the positive factor pairs of 756 are: (1, 756), (2, 378), (3, 252), (4, 189), (6, 126), (9, 84), (12, 63), (18, 42), (27, 28).

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 756 by 1, 756 ÷ 1 = 756.

Step 2: Continue dividing 756 by the numbers until the remainder becomes 0.

756 ÷ 1 = 756

756 ÷ 2 = 378

756 ÷ 3 = 252

756 ÷ 4 = 189

756 ÷ 6 = 126

756 ÷ 9 = 84

756 ÷ 12 = 63

756 ÷ 18 = 42

756 ÷ 27 = 28

Therefore, the factors of 756 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 28, 36, 54, 84, 108, 189, 252, 378, 756.

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

756 ÷ 2 = 378

378 ÷ 2 = 189

189 ÷ 3 = 63

63 ÷ 3 = 21

21 ÷ 3 = 7

7 ÷ 7 = 1

The prime factors of 756 are 2, 3, and 7.

The prime factorization of 756 is: 2² × 3³ × 7.

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

Step 1: Firstly, 756 is divided by 2 to get 378.

Step 2: Now divide 378 by 2 to get 189.

Step 3: Then divide 189 by 3 to get 63.

Step 4: Divide 63 by 3 to get 21.

Step 5: Divide 21 by 3 to get 7.

Here, 7 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 756 is: 2² × 3³ × 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 756: (1, 756), (2, 378), (3, 252), (4, 189), (6, 126), (9, 84), (12, 63), (18, 42), (27, 28).

Negative factor pairs of 756: (-1, -756), (-2, -378), (-3, -252), (-4, -189), (-6, -126), (-9, -84), (-12, -63), (-18, -42), (-27, -28).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 756 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 28, 36, 54, 84, 108, 189, 252, 378, and 756.
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 756.
   
• 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 756 are (1, 756), (2, 378), etc.
   
• Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 756 is 2² × 3³ × 7.
   
• Multiplication method: A method of finding factors by identifying pairs of numbers that can be multiplied to give the original number. For example, using this method, 756 can be expressed as 2 × 378, 3 × 252, etc.