1. Steps to find factors of 123 using Division Method

Example: Find factors of 123

  • Divide 123 by 1: 123 ÷ 1 : Remainder = 0
  • Divide 123 by 3: 123 ÷ 3 : Remainder = 0
  • Divide 123 by 41: 123 ÷ 41 : Remainder = 0
  • Divide 123 by 123: 123 ÷ 123 : Remainder = 0

Hence, Factors of 123 are 1, 3, 41, and 123

2. Steps to find factors of 123 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 123 using the division method, follow these steps:

  • Step 1. Start dividing 123 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 123, which is 3. Divide 123 by 3 to obtain the quotient (41).
    123 ÷ 3 = 41
  • Step 3. Repeat step 1 with the obtained quotient (41).
    41 ÷ 41 = 1

So, the prime factorization of 123 is, 123 = 3 x 41.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 123 as shown below:

So, the prime factorization of 123 is, 123 = 3 x 41.

3. Find factors of 123 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 123 would be the two numbers which, when multiplied, give 123 as the result.

The following table represents the calculation of factors of 123 in pairs:

Factor Pair Pair Factorization
1 and 123 1 x 123 = 123
3 and 41 3 x 41 = 123

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 123. They are called negative pair factors.

Hence, the negative pairs of 123 would be ( -1 , -123 ) , ( -3 , -41 ) .

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

  • Every number is a factor of zero (0), since 123 x 0 = 0.
  • 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, 3, 41, 123 are exact divisors of 123.
  • Factors of 123 are 1, 3, 41, 123. Each factor divides 123 without leaving a remainder.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -123 )?

    Factors of -123 are -1, -3, -41, -123.

  • What is the sum of all factors of 123?

    The sum of all factors of 123 is 168.

  • What is prime factorization of 123?

    Prime factorization of 123 is 3 x 41.

  • What are the pair factors of 123?

    Pair factors of 123 are (1,123), (3,41).

  • What are six multiples of 123?

    First five multiples of 123 are 246, 369, 492, 615, 738, 861.

  • Is 123 a whole number?

    Yes 123 is a whole number.

  • Which is the smallest prime factor of 123?

    Smallest prime factor of 123 is 3.

  • What are five multiples of 123?

    First five multiples of 123 are 246, 369, 492, 615, 738.

  • Write all factors of 123?

    Factors of 123 are 1, 3, 41, 123.

Examples of Factors

Joey wants to write all the prime factors of 123 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 123 are 3, 41.
So in exponential form it can be written as 3 x 41.

How many factors are there for 123?

Factors of 123 are 1, 3, 41, 123.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 123. Can you predict the answer?

3 factor(s) of 123 are 1, 3, 41.

Sammy is puzzled while calculating the prime factors of 123. Can you help him find them?

Factors of 123 are 1, 3, 41, 123.
Prime factors of 123 are 3, 41

What is prime factorization of 123?

Prime factorization of 123 is 3 x 41 = 3 x 41.

Ariel has been assigned the task to find the product of all the prime factors of 123. Can you help her?

Prime factors of 123 are 3, 41.
Hence, the product of prime factors of 123.

Can you help Rubel to find out the product of the even factors of 123?

Factors of 123 are 1, 3, 41, 123.
Even factors of 123 are 0.
Hence, product of even factors of 123 is; 0 = 0.