1. Steps to find factors of 240 using Division Method

Example: Find factors of 240

  • Divide 240 by 1: 240 ÷ 1 : Remainder = 0
  • Divide 240 by 2: 240 ÷ 2 : Remainder = 0
  • Divide 240 by 3: 240 ÷ 3 : Remainder = 0
  • Divide 240 by 4: 240 ÷ 4 : Remainder = 0
  • Divide 240 by 5: 240 ÷ 5 : Remainder = 0
  • Divide 240 by 6: 240 ÷ 6 : Remainder = 0
  • Divide 240 by 8: 240 ÷ 8 : Remainder = 0
  • Divide 240 by 10: 240 ÷ 10 : Remainder = 0
  • Divide 240 by 12: 240 ÷ 12 : Remainder = 0
  • Divide 240 by 15: 240 ÷ 15 : Remainder = 0
  • Divide 240 by 16: 240 ÷ 16 : Remainder = 0
  • Divide 240 by 20: 240 ÷ 20 : Remainder = 0
  • Divide 240 by 24: 240 ÷ 24 : Remainder = 0
  • Divide 240 by 30: 240 ÷ 30 : Remainder = 0
  • Divide 240 by 40: 240 ÷ 40 : Remainder = 0
  • Divide 240 by 48: 240 ÷ 48 : Remainder = 0
  • Divide 240 by 60: 240 ÷ 60 : Remainder = 0
  • Divide 240 by 80: 240 ÷ 80 : Remainder = 0
  • Divide 240 by 120: 240 ÷ 120 : Remainder = 0
  • Divide 240 by 240: 240 ÷ 240 : Remainder = 0

Hence, Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240

2. Steps to find factors of 240 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 240 using the division method, follow these steps:

  • Step 1. Start dividing 240 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 240, which is 2. Divide 240 by 2 to obtain the quotient (120).
    240 ÷ 2 = 120
  • Step 3. Repeat step 1 with the obtained quotient (120).
    120 ÷ 2 = 60
    60 ÷ 2 = 30
    30 ÷ 2 = 15
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So, the prime factorization of 240 is, 240 = 2 x 2 x 2 x 2 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 240 as shown below:

So, the prime factorization of 240 is, 240 = 2 x 2 x 2 x 2 x 3 x 5.

3. Find factors of 240 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 240 would be the two numbers which, when multiplied, give 240 as the result.

The following table represents the calculation of factors of 240 in pairs:

Factor Pair Pair Factorization
1 and 240 1 x 240 = 240
2 and 120 2 x 120 = 240
3 and 80 3 x 80 = 240
4 and 60 4 x 60 = 240
5 and 48 5 x 48 = 240
6 and 40 6 x 40 = 240
8 and 30 8 x 30 = 240
10 and 24 10 x 24 = 240
12 and 20 12 x 20 = 240
15 and 16 15 x 16 = 240

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 240. They are called negative pair factors.

Hence, the negative pairs of 240 would be ( -1 , -240 ) , ( -2 , -120 ) , ( -3 , -80 ) , ( -4 , -60 ) , ( -5 , -48 ) , ( -6 , -40 ) , ( -8 , -30 ) , ( -10 , -24 ) , ( -12 , -20 ) and ( -15 , -16 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 240 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 240.
  • Every number is a factor of zero (0), since 240 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, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 are exact divisors of 240.
  • Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. Each factor divides 240 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 are all less than or equal to 240.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -240 )?

    Factors of -240 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -40, -48, -60, -80, -120, -240.

  • What is the sum of all factors of 240?

    The sum of all factors of 240 is 744.

  • What is prime factorization of 240?

    Prime factorization of 240 is 2 x 2 x 2 x 2 x 3 x 5.

  • What are the pair factors of 240?

    Pair factors of 240 are (1,240), (2,120), (3,80), (4,60), (5,48), (6,40), (8,30), (10,24), (12,20), (15,16).

  • What are six multiples of 240?

    First five multiples of 240 are 480, 720, 960, 1200, 1440, 1680.

  • Is 240 a whole number?

    Yes 240 is a whole number.

  • Which is the smallest prime factor of 240?

    Smallest prime factor of 240 is 2.

  • What are five multiples of 240?

    First five multiples of 240 are 480, 720, 960, 1200, 1440.

  • Write all factors of 240?

    Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.

Examples of Factors

Joey wants to write all the prime factors of 240 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 240 are 2, 2, 2, 2, 3, 5.
So in exponential form it can be written as 24 x 3 x 5.

How many factors are there for 240?

Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
So there are in total 20 factors.

Kevin has been asked to write 19 factor(s) of 240. Can you predict the answer?

19 factor(s) of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120.

Sammy is puzzled while calculating the prime factors of 240. Can you help him find them?

Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
Prime factors of 240 are 2, 2, 2, 2, 3, 5

What is prime factorization of 240?

Prime factorization of 240 is 2 x 2 x 2 x 2 x 3 x 5 = 24 x 3 x 5.

Ariel has been assigned the task to find the product of all the prime factors of 240. Can you help her?

Prime factors of 240 are 2, 2, 2, 2, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 240?

Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
Even factors of 240 are 2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
Hence, product of even factors of 240 is; 2 x 4 x 6 x 8 x 10 x 12 x 16 x 20 x 24 x 30 x 40 x 48 x 60 x 80 x 120 x 240 = 2.8179280429056e+21.