Factors of -210

The numbers that divide -210 evenly are known as factors of -210.

A factor of -210 is a number that divides the number without a remainder.

The factors of -210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

Negative factors of -210: -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105, and -210.

Prime factors of -210: 2, 3, 5, and 7.

Prime factorization of -210: 2 × 3 × 5 × 7.

The sum of factors of 210 (ignoring the sign): 1 + 2 + 3 + 5 + 6 + 7 + 10 + 14 + 15 + 21 + 30 + 35 + 42 + 70 + 105 + 210 = 768

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

• Finding factors using multiplication
   
• Finding factors using the 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 -210. Identifying the numbers which are multiplied to get the number -210 is the multiplication method.

Step 1: Multiply -210 by -1, -210 × -1 = 210.

Step 2: Check for other numbers that give -210 after multiplying:

(-2) × 105 = -210

(-3) × 70 = -210

(-5) × 42 = -210

(-6) × 35 = -210

(-7) × 30 = -210

(-10) × 21 = -210

(-14) × 15 = -210

Therefore, the positive factor pairs of -210 are: (1, -210), (2, -105), (3, -70), (5, -42), (6, -35), (7, -30), (10, -21), (14, -15).

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 -210 by -1, -210 ÷ -1 = 210.

Step 2: Continue dividing -210 by the numbers until the remainder becomes 0.

-210 ÷ -1 = 210

-210 ÷ -2 = 105

-210 ÷ -3 = 70

-210 ÷ -5 = 42

-210 ÷ -6 = 35

-210 ÷ -7 = 30

-210 ÷ -10 = 21

-210 ÷ -14 = 15

Therefore, the factors of -210 are: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.

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 -210 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

210 ÷ 2 = 105

105 ÷ 3 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of -210 are 2, 3, 5, and 7.

The prime factorization of -210 is: 2 × 3 × 5 × 7.

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

Step 1: Firstly, 210 is divided by 2 to get 105.

Step 2: Now divide 105 by 3 to get 35.

Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of -210 is: 2 × 3 × 5 × 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 -210: (1, -210), (2, -105), (3, -70), (5, -42), (6, -35), (7, -30), (10, -21), (14, -15).

Negative factor pairs of -210: (-1, 210), (-2, 105), (-3, 70), (-5, 42), (-6, 35), (-7, 30), (-10, 21), (-14, 15).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
   
• Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of -210.
   
• 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 -210 are (1, -210), (2, -105), etc.
   
• Negative factors: Factors that are negative numbers. For example, -1, -2, -3, -5, etc., are negative factors of -210.
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of -210 is 2 × 3 × 5 × 7.