A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

 

Factors of 648

Factors of 648 are integers that can be divided evenly into 648. There are 20 factors of 648 of which 648 itself is the biggest factor and its prime factors are 2, 3 The sum of all factors of 648 is 1815.

  • All Factors of 648: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324 and 648
  • Prime Factors of 648: 2, 3
  • Prime Factorization of 648: 23 × 34
  • Sum of Factors of 648: 1815
1. What Are the Factors of 648?
2. Factors of 648 by Prime Factorization
3. Factors of 648 in Pairs
4. FAQs on Factors of 648
Factors of 648

What are Factors of 648?

Factors of 648 are pairs of those numbers whose products result in 648. These factors are either prime numbers or composite numbers.

How to Find the Factors of 648?

To find the factors of 648, we will have to find the list of numbers that would divide 648 without leaving any remainder.

  • 648/4 = 162; therefore, 4 is a factor of 648 and 162 is also a factor of 648.
  • 648/9 = 72; therefore, 9 is a factor of 648 and 72 is also a factor of 648.
Similarly we can find other factors. Hence, 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.

☛ Also Check:

Factors of 648 by Prime Factorization

The number 648 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 648. The first step is to divide the number 648 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 648 ÷ 2 = 324
  • 324 ÷ 2 = 162
  • 162 ÷ 2 = 81

Further dividing 81 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 81 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 648 can be written as 23 × 34 where 2, 3 are prime.

 

Factors of 648 in Pairs

Pair factors of 648 are the pairs of numbers that when multiplied give the product 648. The factors of 648 in pairs are:

  • 1 × 648 = (1, 648)
  • 2 × 324 = (2, 324)
  • 3 × 216 = (3, 216)
  • 4 × 162 = (4, 162)
  • 6 × 108 = (6, 108)
  • 8 × 81 = (8, 81)
  • 9 × 72 = (9, 72)
  • 12 × 54 = (12, 54)
  • 18 × 36 = (18, 36)
  • 24 × 27 = (24, 27)

Negative pair factors of 648 are:

  • -1 × -648 = (-1, -648)
  • -2 × -324 = (-2, -324)
  • -3 × -216 = (-3, -216)
  • -4 × -162 = (-4, -162)
  • -6 × -108 = (-6, -108)
  • -8 × -81 = (-8, -81)
  • -9 × -72 = (-9, -72)
  • -12 × -54 = (-12, -54)
  • -18 × -36 = (-18, -36)
  • -24 × -27 = (-24, -27)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 648 Solved Examples

  1. Example 1: How many factors are there for 648?

    Solution:

    The factors of 648 are too many, therefore if we can find the prime factorization of 648, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 648 = 23 × 34
    Therefore, the total number of factors are (3 + 1) × (4 + 1) = 4 × 5 = 20

  2. Example 2: Find the LCM and Greatest Common Factor (GCF) of 648 and 452.

    Solution:

    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 and factors of 452 are 1, 2, 4, 113, 226, 452.

    Therefore, the LCM of 648 and 452 is 73224 and Greatest Common Factor (GCF) of 648 and 452 is 4.

  3. Example 3: Find if 2, 8, 9, 18, 108, 216, 502 and 648 are factors of 648.

    Solution:

    When we divide 648 by 502 it leaves a remainder. Therefore, the number 502 is not a factor of 648. All numbers except 502 are factors of 648.

  4. Example 4: Find the product of all the prime factors of 648.

    Solution:

    Since, the prime factors of 648 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.

Show Solution >

go to slidego to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

 

FAQs on Factors of 648

What are the 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 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, -648.

What is the Sum of all Factors of 648?

Sum of all factors of 648 = (23 + 1 - 1)/(2 - 1) × (34 + 1 - 1)/(3 - 1) = 1815

What Numbers are the Prime Factors of 648?

The prime factors of 648 are 2, 3.

What is the Greatest Common Factor of 648 and 271?

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 and the factors of 271 are 1, 271. 648 and 271 have only one common factor which is 1. This implies that 648 and 271 are co-prime.

Hence, the Greatest Common Factor (GCF) of 648 and 271 is 1.

How Many Factors of 648 are also common to the Factors of 630?

Since, 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 and the factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.
Hence, [1, 2, 3, 6, 9, 18] are the common factors of 648 and 630.

Math worksheets and
visual curriculum