Factors of 138

The numbers that divide 138 evenly are known as factors of 138. A factor of 138 is a number that divides the number without a remainder. The factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.

Negative factors of 138: -1, -2, -3, -6, -23, -46, -69, and -138.

Prime factors of 138: 2, 3, and 23.

Prime factorization of 138: 2 × 3 × 23.

The sum of factors of 138: 1 + 2 + 3 + 6 + 23 + 46 + 69 + 138 = 288

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 138. Identifying the numbers which are multiplied to get the number 138 is the multiplication method.

Step 1: Multiply 138 by 1, 138 × 1 = 138.

Step 2: Check for other numbers that give 138 after multiplying     

2 × 69 = 138     

3 × 46 = 138    

 6 × 23 = 138

Therefore, the positive factor pairs of 138 are: (1, 138), (2, 69), (3, 46), and (6, 23). 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 138 by 1, 138 ÷ 1 = 138.

Step 2: Continue dividing 138 by the numbers until the remainder becomes 0.

138 ÷ 1 = 138

138 ÷ 2 = 69

138 ÷ 3 = 46

138 ÷ 6 = 23

Therefore, the factors of 138 are: 1, 2, 3, 6, 23, 46, 69, 138.

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

138 ÷ 2 = 69

69 ÷ 3 = 23

23 ÷ 23 = 1

The prime factors of 138 are 2, 3, and 23. The prime factorization of 138 is: 2 × 3 × 23.

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

Step 1: Firstly, 138 is divided by 2 to get 69.

Step 2: Now divide 69 by 3 to get 23.

Step 3: 23 is a prime number and cannot be divided further. So, the prime factorization of 138 is: 2 × 3 × 23.

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 138: (1, 138), (2, 69), (3, 46), and (6, 23).
• Negative factor pairs of 138: (-1, -138), (-2, -69), (-3, -46), and (-6, -23).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 23 are prime factors of 138.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are factor pairs. For example, the factor pairs of 138 are (1, 138), (2, 69), etc.

• Prime factorization: The process of expressing a number as a product of its prime factors. For instance, the prime factorization of 138 is 2 × 3 × 23.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method, we find that 6 × 23 = 138.