1. Steps to find factors of 468 using Division Method

Example: Find factors of 468

  • Divide 468 by 1: 468 ÷ 1 : Remainder = 0
  • Divide 468 by 2: 468 ÷ 2 : Remainder = 0
  • Divide 468 by 3: 468 ÷ 3 : Remainder = 0
  • Divide 468 by 4: 468 ÷ 4 : Remainder = 0
  • Divide 468 by 6: 468 ÷ 6 : Remainder = 0
  • Divide 468 by 9: 468 ÷ 9 : Remainder = 0
  • Divide 468 by 12: 468 ÷ 12 : Remainder = 0
  • Divide 468 by 13: 468 ÷ 13 : Remainder = 0
  • Divide 468 by 18: 468 ÷ 18 : Remainder = 0
  • Divide 468 by 26: 468 ÷ 26 : Remainder = 0
  • Divide 468 by 36: 468 ÷ 36 : Remainder = 0
  • Divide 468 by 39: 468 ÷ 39 : Remainder = 0
  • Divide 468 by 52: 468 ÷ 52 : Remainder = 0
  • Divide 468 by 78: 468 ÷ 78 : Remainder = 0
  • Divide 468 by 117: 468 ÷ 117 : Remainder = 0
  • Divide 468 by 156: 468 ÷ 156 : Remainder = 0
  • Divide 468 by 234: 468 ÷ 234 : Remainder = 0
  • Divide 468 by 468: 468 ÷ 468 : Remainder = 0

Hence, Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, and 468

2. Steps to find factors of 468 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 468 using the division method, follow these steps:

  • Step 1. Start dividing 468 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 468, which is 2. Divide 468 by 2 to obtain the quotient (234).
    468 ÷ 2 = 234
  • Step 3. Repeat step 1 with the obtained quotient (234).
    234 ÷ 2 = 117
    117 ÷ 3 = 39
    39 ÷ 3 = 13
    13 ÷ 13 = 1

So, the prime factorization of 468 is, 468 = 2 x 2 x 3 x 3 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 468 as shown below:

So, the prime factorization of 468 is, 468 = 2 x 2 x 3 x 3 x 13.

3. Find factors of 468 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 468 would be the two numbers which, when multiplied, give 468 as the result.

The following table represents the calculation of factors of 468 in pairs:

Factor Pair Pair Factorization
1 and 468 1 x 468 = 468
2 and 234 2 x 234 = 468
3 and 156 3 x 156 = 468
4 and 117 4 x 117 = 468
6 and 78 6 x 78 = 468
9 and 52 9 x 52 = 468
12 and 39 12 x 39 = 468
13 and 36 13 x 36 = 468
18 and 26 18 x 26 = 468

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 468. They are called negative pair factors.

Hence, the negative pairs of 468 would be ( -1 , -468 ) , ( -2 , -234 ) , ( -3 , -156 ) , ( -4 , -117 ) , ( -6 , -78 ) , ( -9 , -52 ) , ( -12 , -39 ) , ( -13 , -36 ) and ( -18 , -26 ) .

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. 468 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 468.
  • Every number is a factor of zero (0), since 468 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, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 are exact divisors of 468.
  • Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468. Each factor divides 468 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 are all less than or equal to 468.

Frequently Asked Questions

  • Which is the smallest prime factor of 468?

    Smallest prime factor of 468 is 2.

  • Is 468 a perfect square?

    No 468 is not a perfect square.

  • What are five multiples of 468?

    First five multiples of 468 are 936, 1404, 1872, 2340, 2808.

  • What is prime factorization of 468?

    Prime factorization of 468 is 2 x 2 x 3 x 3 x 13.

  • What are factors of 468?

    Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.

  • How do you find factors of a negative number? ( eg. -468 )?

    Factors of -468 are -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468.

  • Is 468 a whole number?

    Yes 468 is a whole number.

  • Which is greatest factor of 468?

    The greatest factor of 468 is 234.

  • What are the prime factors of 468?

    The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
    Prime factors of 468 are 2, 2, 3, 3, 13.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 468. Can you help her?

Prime factors of 468 are 2, 2, 3, 3, 13.
Hence, the product of prime factors of 78.

Can you help Rubel to find out the product of the even factors of 468?

Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
Even factors of 468 are 2, 4, 6, 12, 18, 26, 36, 52, 78, 156, 234, 468.
Hence, product of even factors of 468 is; 2 x 4 x 6 x 12 x 18 x 26 x 36 x 52 x 78 x 156 x 234 x 468 = 672442404508532700.

Joy wants to calculate mean of all the factors of 468. Help him in finding the mean of 468.

Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 468 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 13 + 18 + 26 + 36 + 39 + 52 + 78 + 117 + 156 + 234 + 468 = 1274.
Hence, the mean of factors of 468 is 1274 ÷ 18 = 70.78.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 468? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468.

How many factors are there for 468?

Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
So there are in total 18 factors.

Joey wants to write all the prime factors of 468 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 468 are 2, 2, 3, 3, 13.
So in exponential form it can be written as 22 x 32 x 13.

Kevin has been asked to write 17 factor(s) of 468. Can you predict the answer?

17 factor(s) of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234.