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Factors of 660

Factors of 660 are integers that can be divided evenly into 660. It has total 24 factors of which 660 is the biggest factor and the prime factors of 660 are 2, 3, 5, 11. The Prime Factorization of 660 is 22 × 31 × 51 × 111.

  • All Factors of 660: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330 and 660
  • Prime Factors of 660: 2, 3, 5, 11
  • Prime Factorization of 660: 22 × 31 × 51 × 111
  • Sum of Factors of 660: 2016
1. What Are the Factors of 660?
2. Factors of 660 by Prime Factorization
3. Factors of 660 in Pairs
4. FAQs on Factors of 660
Factors of 660

What are Factors of 660?

Factors of 660 are pairs of those numbers whose products result in 660. These factors are either prime numbers or composite numbers.

How to Find the Factors of 660?

To find the factors of 660, we will have to find the list of numbers that would divide 660 without leaving any remainder.

  • 660/5 = 132; therefore, 5 is a factor of 660 and 132 is also a factor of 660.
  • 660/11 = 60; therefore, 11 is a factor of 660 and 60 is also a factor of 660.
Similarly we can find other factors. Hence, the factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660.

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Factors of 660 by Prime Factorization

The number 660 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 660. The first step is to divide the number 660 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 660 ÷ 2 = 330
  • 330 ÷ 2 = 165

Further dividing 165 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 165 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 660 can be written as 22 × 31 × 51 × 111 where 2, 3, 5, 11 are prime.

 

Factors of 660 in Pairs

Pair factors of 660 are the pairs of numbers that when multiplied give the product 660. The factors of 660 in pairs are:

  • 1 × 660 = (1, 660)
  • 2 × 330 = (2, 330)
  • 3 × 220 = (3, 220)
  • 4 × 165 = (4, 165)
  • 5 × 132 = (5, 132)
  • 6 × 110 = (6, 110)
  • 10 × 66 = (10, 66)
  • 11 × 60 = (11, 60)
  • 12 × 55 = (12, 55)
  • 15 × 44 = (15, 44)
  • 20 × 33 = (20, 33)
  • 22 × 30 = (22, 30)

Negative pair factors of 660 are:

  • -1 × -660 = (-1, -660)
  • -2 × -330 = (-2, -330)
  • -3 × -220 = (-3, -220)
  • -4 × -165 = (-4, -165)
  • -5 × -132 = (-5, -132)
  • -6 × -110 = (-6, -110)
  • -10 × -66 = (-10, -66)
  • -11 × -60 = (-11, -60)
  • -12 × -55 = (-12, -55)
  • -15 × -44 = (-15, -44)
  • -20 × -33 = (-20, -33)
  • -22 × -30 = (-22, -30)

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

Factors of 660 Solved Examples

  1. Example 1: How many factors are there for 660?

    Solution:

    The factors of 660 are too many, therefore if we can find the prime factorization of 660, 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 660 = 22 × 31 × 51 × 111
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 660 and 462.

    Solution:

    The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660 and factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.

    Therefore, the Lowest Common Multiple (LCM) of 660 and 462 is 4620 and Greatest Common Divisor (GCD) of 660 and 462 is 66.

  3. Example 3: Find if 4, 6, 10, 66, 132, 165, 330 and 591 are factors of 660.

    Solution:

    When we divide 660 by 591 it leaves a remainder. Therefore, the number 591 is not a factor of 660. All numbers except 591 are factors of 660.

  4. Example 4: Find the product of all the prime factors of 660.

    Solution:

    Since, the prime factors of 660 are 2, 3, 5, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 11 = 330.

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FAQs on Factors of 660

What are the Factors of 660?

The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660 and its negative factors are -1, -2, -3, -4, -5, -6, -10, -11, -12, -15, -20, -22, -30, -33, -44, -55, -60, -66, -110, -132, -165, -220, -330, -660.

What is the Sum of the Factors of 660?

Sum of all factors of 660 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 2016

What are Prime Factors of 660?

The prime factors of 660 are 2, 3, 5, 11.

What is the Greatest Common Factor of 660 and 583?

The factors of 660 and 583 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660 and 1, 11, 53, 583 respectively.

Common factors of 660 and 583 are [1, 11].

Hence, the Greatest Common Factor (GCF) of 660 and 583 is 11.

How Many Factors of 452 are also common to the Factors of 660?

Since, the factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660 and the factors of 452 are 1, 2, 4, 113, 226, 452.
Hence, [1, 2, 4] are the common factors of 660 and 452.

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