1. Steps to find factors of 106 using Division Method

Example: Find factors of 106

  • Divide 106 by 1: 106 ÷ 1 : Remainder = 0
  • Divide 106 by 2: 106 ÷ 2 : Remainder = 0
  • Divide 106 by 53: 106 ÷ 53 : Remainder = 0
  • Divide 106 by 106: 106 ÷ 106 : Remainder = 0

Hence, Factors of 106 are 1, 2, 53, and 106

2. Steps to find factors of 106 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 106 using the division method, follow these steps:

  • Step 1. Start dividing 106 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 106, which is 2. Divide 106 by 2 to obtain the quotient (53).
    106 ÷ 2 = 53
  • Step 3. Repeat step 1 with the obtained quotient (53).
    53 ÷ 53 = 1

So, the prime factorization of 106 is, 106 = 2 x 53.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 106 as shown below:

So, the prime factorization of 106 is, 106 = 2 x 53.

3. Find factors of 106 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 106 would be the two numbers which, when multiplied, give 106 as the result.

The following table represents the calculation of factors of 106 in pairs:

Factor Pair Pair Factorization
1 and 106 1 x 106 = 106
2 and 53 2 x 53 = 106

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 106. They are called negative pair factors.

Hence, the negative pairs of 106 would be ( -1 , -106 ) , ( -2 , -53 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 106 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, 53, 106 are exact divisors of 106.
  • 1 is a factor of every number. Eg. 1 is a factor of 106.
  • Every number is a factor of zero (0), since 106 x 0 = 0.

Frequently Asked Questions

  • Which is the smallest prime factor of 106?

    The smallest prime factor of 106 is 2.

  • Is 106 a whole number?

    Yes 106 is a whole number.

  • What are the prime factors of 106?

    The factors of 106 are 1, 2, 53, 106.
    Prime factors of 106 are 2, 53.

  • What two numbers make 106?

    Two numbers that make 106 are 2 and 53.

  • What are multiples of 106?

    First five multiples of 106 are 212, 318, 424, 530.

  • What is the sum of all factors of 106?

    The sum of all factors of 106 is 162.

  • What are five multiples of 106?

    First five multiples of 106 are 212, 318, 424, 530, 636.

  • Is 106 a perfect square?

    No 106 is not a perfect square.

  • What is the greatest prime factors of 106?

    The greatest prime factor of 106 is 53.

Examples of Factors

How many factors are there for 106?

Factors of 106 are 1, 2, 53, 106.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 106. Can you predict the answer?

3 factor(s) of 106 are 1, 2, 53.

Sammy is puzzled while calculating the prime factors of 106. Can you help him find them?

Factors of 106 are 1, 2, 53, 106.
Prime factors of 106 are 2, 53

What is prime factorization of 106?

Prime factorization of 106 is 2 x 53 = 2 x 53.

Ariel has been assigned the task to find the product of all the prime factors of 106. Can you help her?

Prime factors of 106 are 2, 53.
Hence, the product of prime factors of 106.

Can you help Rubel to find out the product of the even factors of 106?

Factors of 106 are 1, 2, 53, 106.
Even factors of 106 are 2, 106.
Hence, product of even factors of 106 is; 2 x 106 = 212.

Joy wants to calculate mean of all the factors of 106. Help him in finding the mean of 106.

Factors of 106 are 1, 2, 53, 106.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 106 is 1 + 2 + 53 + 106 = 162.
Hence, the mean of factors of 106 is 162 ÷ 4 = 40.50.