1. Steps to find factors of 648 using Division Method

Example: Find factors of 648

  • Divide 648 by 1: 648 ÷ 1 : Remainder = 0
  • Divide 648 by 2: 648 ÷ 2 : Remainder = 0
  • Divide 648 by 3: 648 ÷ 3 : Remainder = 0
  • Divide 648 by 4: 648 ÷ 4 : Remainder = 0
  • Divide 648 by 6: 648 ÷ 6 : Remainder = 0
  • Divide 648 by 8: 648 ÷ 8 : Remainder = 0
  • Divide 648 by 9: 648 ÷ 9 : Remainder = 0
  • Divide 648 by 12: 648 ÷ 12 : Remainder = 0
  • Divide 648 by 18: 648 ÷ 18 : Remainder = 0
  • Divide 648 by 24: 648 ÷ 24 : Remainder = 0
  • Divide 648 by 27: 648 ÷ 27 : Remainder = 0
  • Divide 648 by 36: 648 ÷ 36 : Remainder = 0
  • Divide 648 by 54: 648 ÷ 54 : Remainder = 0
  • Divide 648 by 72: 648 ÷ 72 : Remainder = 0
  • Divide 648 by 81: 648 ÷ 81 : Remainder = 0
  • Divide 648 by 108: 648 ÷ 108 : Remainder = 0
  • Divide 648 by 162: 648 ÷ 162 : Remainder = 0
  • Divide 648 by 216: 648 ÷ 216 : Remainder = 0
  • Divide 648 by 324: 648 ÷ 324 : Remainder = 0
  • Divide 648 by 648: 648 ÷ 648 : Remainder = 0

Hence, Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648

2. Steps to find factors of 648 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 648 using the division method, follow these steps:

  • Step 1. Start dividing 648 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 648, which is 2. Divide 648 by 2 to obtain the quotient (324).
    648 ÷ 2 = 324
  • Step 3. Repeat step 1 with the obtained quotient (324).
    324 ÷ 2 = 162
    162 ÷ 2 = 81
    81 ÷ 3 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 648 is, 648 = 2 x 2 x 2 x 3 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 648 as shown below:

So, the prime factorization of 648 is, 648 = 2 x 2 x 2 x 3 x 3 x 3 x 3.

3. Find factors of 648 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 648 would be the two numbers which, when multiplied, give 648 as the result.

The following table represents the calculation of factors of 648 in pairs:

Factor Pair Pair Factorization
1 and 648 1 x 648 = 648
2 and 324 2 x 324 = 648
3 and 216 3 x 216 = 648
4 and 162 4 x 162 = 648
6 and 108 6 x 108 = 648
8 and 81 8 x 81 = 648
9 and 72 9 x 72 = 648
12 and 54 12 x 54 = 648
18 and 36 18 x 36 = 648
24 and 27 24 x 27 = 648

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 648. They are called negative pair factors.

Hence, the negative pairs of 648 would be ( -1 , -648 ) , ( -2 , -324 ) , ( -3 , -216 ) , ( -4 , -162 ) , ( -6 , -108 ) , ( -8 , -81 ) , ( -9 , -72 ) , ( -12 , -54 ) , ( -18 , -36 ) and ( -24 , -27 ) .

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. 648 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 648.
  • Every number is a factor of zero (0), since 648 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, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are exact divisors of 648.
  • Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. Each factor divides 648 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648 are all less than or equal to 648.

Frequently Asked Questions

  • Which is the smallest prime factor of 648?

    Smallest prime factor of 648 is 2.

  • Is 648 a perfect square?

    No 648 is not a perfect square.

  • What are five multiples of 648?

    First five multiples of 648 are 1296, 1944, 2592, 3240, 3888.

  • What is prime factorization of 648?

    Prime factorization of 648 is 2 x 2 x 2 x 3 x 3 x 3 x 3.

  • What are factors of 648?

    Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.

  • How do you find factors of a negative number? ( eg. -648 )?

    Factors of -648 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, -648.

  • Is 648 a whole number?

    Yes 648 is a whole number.

  • Which is greatest factor of 648?

    The greatest factor of 648 is 324.

  • What are the prime factors of 648?

    The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
    Prime factors of 648 are 2, 2, 2, 3, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 648. Can you help her?

Prime factors of 648 are 2, 2, 2, 3, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 648?

Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
Even factors of 648 are 2, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 648.
Hence, product of even factors of 648 is; 2 x 4 x 6 x 8 x 12 x 18 x 24 x 36 x 54 x 72 x 108 x 162 x 216 x 324 x 648 = 2.2107391972073336e+23.

Joy wants to calculate mean of all the factors of 648. Help him in finding the mean of 648.

Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 648 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 324 + 648 = 1815.
Hence, the mean of factors of 648 is 1815 ÷ 20 = 90.75.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 648? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, -648.

How many factors are there for 648?

Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.
So there are in total 20 factors.

Joey wants to write all the prime factors of 648 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 648 are 2, 2, 2, 3, 3, 3, 3.
So in exponential form it can be written as 23 x 34.

Kevin has been asked to write 19 factor(s) of 648. Can you predict the answer?

19 factor(s) of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324.