Factors of -72

The numbers that divide -72 evenly are known as factors of -72.

A factor of -72 is a number that divides the number without remainder.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Negative factors of -72: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.

Prime factors of 72: 2 and 3.

Prime factorization of 72: 2³ × 3².

The sum of factors of 72: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72 = 192

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 72. Identifying the numbers which are multiplied to get the number 72 is the multiplication method.

Step 1: Multiply 72 by 1, 72 × 1 = 72.

Step 2: Check for other numbers that give 72 after multiplying 2 × 36 = 72 3 × 24 = 72 4 × 18 = 72 6 × 12 = 72 8 × 9 = 72

Therefore, the positive factor pairs of 72 are: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9).

All these factor pairs result in 72.

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 72 by 1, 72 ÷ 1 = 72.

Step 2: Continue dividing 72 by the numbers until the remainder becomes 0.

72 ÷ 1 = 72

72 ÷ 2 = 36

72 ÷ 3 = 24

72 ÷ 4 = 18

72 ÷ 6 = 12

72 ÷ 8 = 9

Therefore, the factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

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

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of 72 are 2 and 3.

The prime factorization of 72 is: 2³ × 3².

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

Step 1: Firstly, 72 is divided by 2 to get 36.

Step 2: Now divide 36 by 2 to get 18.

Step 3: Then divide 18 by 2 to get 9.

Step 4: Divide 9 by 3 to get 3.

Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 72 is: 2³ × 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 72: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9).

Negative factor pairs of -72: (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), and (-8, -9).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

• Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 72.

• 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 72 are (1, 72), (2, 36), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 72 is 2³ × 3².

• Negative factors: The negative counterparts of the positive factors. For example, the negative factors of -72 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, and -72.