Factors of -70

The numbers that divide -70 evenly are known as factors of -70.

A factor of -70 is a number that divides the number without remainder.

The positive factors of 70: 1, 2, 5, 7, 10, 14, 35, and 70.

 Negative factors of -70: -1, -2, -5, -7, -10, -14, -35, and -70.

Prime factors of 70: 2, 5, and 7.

Prime factorization of 70: 2 × 5 × 7.

The sum of the positive factors of 70: 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144

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 70. Identifying the numbers that are multiplied to get the number 70 is the multiplication method.

Step 1: Multiply 70 by 1, 70 × 1 = 70.

Step 2: Check for other numbers that give 70 after multiplying 2 × 35 = 70 5 × 14 = 70 7 × 10 = 70

Therefore, the positive factor pairs of 70 are: (1, 70), (2, 35), (5, 14), (7, 10).

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 that result in whole numbers as factors. Factors can be calculated by following the simple division method 

Step 1: Divide 70 by 1, 70 ÷ 1 = 70.

Step 2: Continue dividing 70 by the numbers until the remainder becomes 0.

70 ÷ 1 = 70

70 ÷ 2 = 35

70 ÷ 5 = 14

70 ÷ 7 = 10

Therefore, the factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70.

The factors can be found by dividing 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 70 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

70 ÷ 2 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of 70 are 2, 5, and 7.

The prime factorization of 70 is: 2 × 5 × 7.

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

Step 1: Firstly, 70 is divided by 2 to get 35.

Step 2: Now divide 35 by 5 to get 7.

Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 70 is: 2 × 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 70: (1, 70), (2, 35), (5, 14), and (7, 10).

Negative factor pairs of -70: (-1, -70), (-2, -35), (-5, -14), and (-7, -10).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

• Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 70.

• 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 70 are (1, 70), (2, 35), etc.

• Negative factors: The negative counterparts of each positive factor of a given number. For example, the negative factors of -70 are -1, -2, -5, etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 70 is 2 × 5 × 7.