1. Steps to find factors of 138 using Division Method

Example: Find factors of 138

  • Divide 138 by 1: 138 ÷ 1 : Remainder = 0
  • Divide 138 by 2: 138 ÷ 2 : Remainder = 0
  • Divide 138 by 3: 138 ÷ 3 : Remainder = 0
  • Divide 138 by 6: 138 ÷ 6 : Remainder = 0
  • Divide 138 by 23: 138 ÷ 23 : Remainder = 0
  • Divide 138 by 46: 138 ÷ 46 : Remainder = 0
  • Divide 138 by 69: 138 ÷ 69 : Remainder = 0
  • Divide 138 by 138: 138 ÷ 138 : Remainder = 0

Hence, Factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138

2. Steps to find factors of 138 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 138 using the division method, follow these steps:

  • Step 1. Start dividing 138 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 138, which is 2. Divide 138 by 2 to obtain the quotient (69).
    138 ÷ 2 = 69
  • Step 3. Repeat step 1 with the obtained quotient (69).
    69 ÷ 3 = 23
    23 ÷ 23 = 1

So, the prime factorization of 138 is, 138 = 2 x 3 x 23.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 138 as shown below:

So, the prime factorization of 138 is, 138 = 2 x 3 x 23.

3. Find factors of 138 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 138 would be the two numbers which, when multiplied, give 138 as the result.

The following table represents the calculation of factors of 138 in pairs:

Factor Pair Pair Factorization
1 and 138 1 x 138 = 138
2 and 69 2 x 69 = 138
3 and 46 3 x 46 = 138
6 and 23 6 x 23 = 138

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 138. They are called negative pair factors.

Hence, the negative pairs of 138 would be ( -1 , -138 ) , ( -2 , -69 ) , ( -3 , -46 ) and ( -6 , -23 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 138 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 6, 23, 46, 69, 138 are exact divisors of 138.
  • 1 is a factor of every number. Eg. 1 is a factor of 138.
  • Every number is a factor of zero (0), since 138 x 0 = 0.

Frequently Asked Questions

  • What are the prime factors of 138?

    The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138.
    Prime factors of 138 are 2, 3, 23.

  • What two numbers make 138?

    Two numbers that make 138 are 2 and 69.

  • What is the greatest prime factors of 138?

    The greatest prime factor of 138 is 23.

  • What are factors of 138?

    Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138.

  • How do you find factors of a negative number? ( eg. -138 )?

    Factors of -138 are -1, -2, -3, -6, -23, -46, -69, -138.

  • What are five multiples of 138?

    First five multiples of 138 are 276, 414, 552, 690, 828.

  • Write some multiples of 138?

    First five multiples of 138 are 276, 414, 552, 690.

  • Is 138 a perfect square?

    No 138 is not a perfect square.

  • What two numbers make 138?

    Two numbers that make 138 are 2 and 69.

Examples of Factors

What is prime factorization of 138?

Prime factorization of 138 is 2 x 3 x 23 = 2 x 3 x 23.

Sammy is puzzled while calculating the prime factors of 138. Can you help him find them?

Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138.
Prime factors of 138 are 2, 3, 23

Kevin has been asked to write 7 factor(s) of 138. Can you predict the answer?

7 factor(s) of 138 are 1, 2, 3, 6, 23, 46, 69.

Joey wants to write all the prime factors of 138 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 138 are 2, 3, 23.
So in exponential form it can be written as 2 x 3 x 23.

How many factors are there for 138?

Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 138? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 23, 46, 69, 138.
Negative factors are -1, -2, -3, -6, -23, -46, -69, -138.

Can you help Rubel to find out the product of the even factors of 138?

Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138.
Even factors of 138 are 2, 6, 46, 138.
Hence, product of even factors of 138 is; 2 x 6 x 46 x 138 = 76176.