Factors of -39

The numbers that divide -39 evenly are known as factors of -39.

A factor of -39 is a number that divides the number without a remainder.

The factors of -39 are 1, -1, 3, -3, 13, -13, 39, and -39.

Prime factors of -39: 3 and 13.

Prime factorization of -39: -1 × 3 × 13.

The sum of positive factors of 39: 1 + 3 + 13 + 39 = 56

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 -39. Identifying the numbers which are multiplied to get the number -39 is the multiplication method.

Step 1: Multiply -39 by 1, -39 × 1 = -39.

Step 2: Check for other numbers that give -39 after multiplying:

-1 × 39 = -39

3 × -13 = -39

-3 × 13 = -39

Therefore, the factor pairs of -39 are: (1, -39), (-1, 39), (3, -13), and (-3, 13).

Dividing the given numbers by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method:

Step 1: Divide -39 by 1,

-39 ÷ 1 = -39.

Step 2: Continue dividing -39 by the numbers until the remainder becomes 0.

-39 ÷ 1 = -39

-39 ÷ 3 = -13

-39 ÷ 13 = -3

-39 ÷ 39 = -1

Therefore, the factors of -39 are: 1, -1, 3, -3, 13, -13, 39, and -39.

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 -39 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.

-39 ÷ -1 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of -39 are 3 and 13.

The prime factorization of -39 is: -1 × 3 × 13.

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

Step 1: Firstly, -39 is divided by -1 to get 39.

Step 2: Now divide 39 by 3 to get 13. Here, 13 is a prime number, that cannot be divided anymore.

So, the prime factorization of -39 is: -1 × 3 × 13.

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

Factor pairs of -39: (1, -39), (-1, 39), (3, -13), and (-3, 13).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -39 are 1, -1, 3, -3, 13, -13, 39, and -39.

• Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of -39.

• 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 -39 are (1, -39), (-1, 39), etc.

• Prime factorization: Breaking down a number into its smallest prime factors. For example, the prime factorization of -39 is -1 × 3 × 13.

• Absolute value: The distance of a number from zero on the number line, without considering which direction from zero the number lies. For example, the absolute value of -39 is 39.