Factors of -252

The numbers that divide -252 evenly are known as factors of -252.

A factor of -252 is a number that divides the number without remainder.

The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.

Negative factors of -252: -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, and -252.

Prime factors of 252: 2, 3, and 7.

Prime factorization of 252: 2² × 3² × 7.

The sum of factors of 252: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 + 252 = 936

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 252. Identifying the numbers which are multiplied to get the number 252 is the multiplication method.

Step 1: Multiply 252 by 1, 252 × 1 = 252.

Step 2: Check for other numbers that give 252 after multiplying:

2 × 126 = 252

3 × 84 = 252

4 × 63 = 252

6 × 42 = 252

7 × 36 = 252

9 × 28 = 252

12 × 21 = 252

14 × 18 = 252

Therefore, the positive factor pairs of 252 are: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18).

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 252 by 1, 252 ÷ 1 = 252.

Step 2: Continue dividing 252 by the numbers until the remainder becomes 0.

252 ÷ 1 = 252

252 ÷ 2 = 126

252 ÷ 3 = 84

252 ÷ 4 = 63

252 ÷ 6 = 42

252 ÷ 7 = 36

252 ÷ 9 = 28

252 ÷ 12 = 21

252 ÷ 14 = 18

Therefore, the factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

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

252 ÷ 2 = 126

126 ÷ 2 = 63

63 ÷ 3 = 21

21 ÷ 3 = 7

7 ÷ 7 = 1

The prime factors of 252 are 2, 3, and 7.

The prime factorization of 252 is: 2² × 3² × 7.

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

Step 1: Firstly, 252 is divided by 2 to get 126.

Step 2: Now divide 126 by 2 to get 63.

Step 3: Then divide 63 by 3 to get 21.

Step 4: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 252 is: 2² × 3² × 7.

Factor Pairs: Two numbers that are multiplied to give a specific number are called as factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 252: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18).

Negative factor pairs of -252: (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28), (-12, -21), (-14, -18).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of -252.
   
• 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 -252 are (1, 252), (2, 126), etc.
   
• Negative factors: Factors that are negative, dividing the number evenly. For example, -1, -2, -3, -4, etc., are negative factors of -252.
   
• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of -252 is 2² × 3² × 7.