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Factors of 672

Factors of 672 are the list of integers that can be evenly divided into 672. There are total 24 factors of 672, of which 2, 3, 7 are its prime factors. The Prime Factorization of 672 is 25 × 31 × 71.

  • All Factors of 672: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336 and 672
  • Prime Factors of 672: 2, 3, 7
  • Prime Factorization of 672: 25 × 31 × 71
  • Sum of Factors of 672: 2016
1. What Are the Factors of 672?
2. Factors of 672 by Prime Factorization
3. Factors of 672 in Pairs
4. FAQs on Factors of 672
Factors of 672

What are Factors of 672?

Factors of 672 are pairs of those numbers whose products result in 672. These factors are either prime numbers or composite numbers.

How to Find the Factors of 672?

To find the factors of 672, we will have to find the list of numbers that would divide 672 without leaving any remainder.

  • 672/3 = 224; therefore, 3 is a factor of 672 and 224 is also a factor of 672.
  • 672/56 = 12; therefore, 56 is a factor of 672 and 12 is also a factor of 672.
Similarly we can find other factors. Hence, the factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672.

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Factors of 672 by Prime Factorization

The number 672 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 672. The first step is to divide the number 672 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 672 ÷ 2 = 336
  • 336 ÷ 2 = 168
  • 168 ÷ 2 = 84
  • 84 ÷ 2 = 42
  • 42 ÷ 2 = 21

Further dividing 21 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 21 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 672 can be written as 25 × 31 × 71 where 2, 3, 7 are prime.

 

Factors of 672 in Pairs

Pair factors of 672 are the pairs of numbers that when multiplied give the product 672. The factors of 672 in pairs are:

  • 1 × 672 = (1, 672)
  • 2 × 336 = (2, 336)
  • 3 × 224 = (3, 224)
  • 4 × 168 = (4, 168)
  • 6 × 112 = (6, 112)
  • 7 × 96 = (7, 96)
  • 8 × 84 = (8, 84)
  • 12 × 56 = (12, 56)
  • 14 × 48 = (14, 48)
  • 16 × 42 = (16, 42)
  • 21 × 32 = (21, 32)
  • 24 × 28 = (24, 28)

Negative pair factors of 672 are:

  • -1 × -672 = (-1, -672)
  • -2 × -336 = (-2, -336)
  • -3 × -224 = (-3, -224)
  • -4 × -168 = (-4, -168)
  • -6 × -112 = (-6, -112)
  • -7 × -96 = (-7, -96)
  • -8 × -84 = (-8, -84)
  • -12 × -56 = (-12, -56)
  • -14 × -48 = (-14, -48)
  • -16 × -42 = (-16, -42)
  • -21 × -32 = (-21, -32)
  • -24 × -28 = (-24, -28)

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

Factors of 672 Solved Examples

  1. Example 1: How many factors are there for 672?

    Solution:

    The factors of 672 are too many, therefore if we can find the prime factorization of 672, 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 672 = 25 × 31 × 71
    Therefore, the total number of factors are (5 + 1) × (1 + 1) × (1 + 1) = 6 × 2 × 2 = 24

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 672 and 600.

    Solution:

    The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 and factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.

    Therefore, the LCM of 672 and 600 is 16800 and Greatest Common Divisor (GCD) of 672 and 600 is 24.

  3. Example 3: Find if 1, 7, 14, 24, 48, 56, 377 and 672 are factors of 672.

    Solution:

    When we divide 672 by 377 it leaves a remainder. Therefore, the number 377 is not a factor of 672. All numbers except 377 are factors of 672.

  4. Example 4: Find the product of all the prime factors of 672.

    Solution:

    Since, the prime factors of 672 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

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FAQs on Factors of 672

What are the Factors of 672?

The factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 and its negative factors are -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -32, -42, -48, -56, -84, -96, -112, -168, -224, -336, -672.

What is the Sum of all the Factors of 672?

Sum of all factors of 672 = (25 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) = 2016

What are Prime Factors of 672?

The prime factors of 672 are 2, 3, 7.

What is the Greatest Common Factor of 672 and 27?

The factors of 672 and 27 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 and 1, 3, 9, 27 respectively.

Common factors of 672 and 27 are [1, 3].

Hence, the GCF of 672 and 27 is 3.

How Many Factors of 672 are also Factors of 291?

Since, the factors of 672 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672 and the factors of 291 are 1, 3, 97, 291.
Hence, [1, 3] are the common factors of 672 and 291.

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