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Factors of 2625

Factors of 2625 are the list of integers that we can split evenly into 2625. There are overall 16 factors of 2625 among which 2625 is the biggest factor and its prime factors are 3, 5, 7. The Prime Factorization of 2625 is 31 × 53 × 71.

  • All Factors of 2625: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875 and 2625
  • Prime Factors of 2625: 3, 5, 7
  • Prime Factorization of 2625: 31 × 53 × 71
  • Sum of Factors of 2625: 4992
1. What Are the Factors of 2625?
2. Factors of 2625 by Prime Factorization
3. Factors of 2625 in Pairs
4. FAQs on Factors of 2625
Factors of 2625

What are Factors of 2625?

Factors of 2625 are pairs of those numbers whose products result in 2625. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2625?

To find the factors of 2625, we will have to find the list of numbers that would divide 2625 without leaving any remainder.

  • 2625/7 = 375; therefore, 7 is a factor of 2625 and 375 is also a factor of 2625.
  • 2625/105 = 25; therefore, 105 is a factor of 2625 and 25 is also a factor of 2625.
Similarly we can find other factors. Hence, the factors of 2625 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625.

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Factors of 2625 by Prime Factorization

The number 2625 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2625. The first step is to divide the number 2625 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 2625 ÷ 3 = 875

Further dividing 875 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 875 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 2625 can be written as 31 × 53 × 71 where 3, 5, 7 are prime.

 

Factors of 2625 in Pairs

Pair factors of 2625 are the pairs of numbers that when multiplied give the product 2625. The factors of 2625 in pairs are:

  • 1 × 2625 = (1, 2625)
  • 3 × 875 = (3, 875)
  • 5 × 525 = (5, 525)
  • 7 × 375 = (7, 375)
  • 15 × 175 = (15, 175)
  • 21 × 125 = (21, 125)
  • 25 × 105 = (25, 105)
  • 35 × 75 = (35, 75)

Negative pair factors of 2625 are:

  • -1 × -2625 = (-1, -2625)
  • -3 × -875 = (-3, -875)
  • -5 × -525 = (-5, -525)
  • -7 × -375 = (-7, -375)
  • -15 × -175 = (-15, -175)
  • -21 × -125 = (-21, -125)
  • -25 × -105 = (-25, -105)
  • -35 × -75 = (-35, -75)

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

Factors of 2625 Solved Examples

  1. Example 1: How many factors are there for 2625?

    Solution:

    The factors of 2625 are too many, therefore if we can find the prime factorization of 2625, 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 2625 = 31 × 53 × 71
    Therefore, the total number of factors are (1 + 1) × (3 + 1) × (1 + 1) = 2 × 4 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 2625 and 673.

    Solution:

    The factors of 2625 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625 and factors of 673 are 1, 673.

    Therefore, the Lowest Common Multiple (LCM) of 2625 and 673 is 1766625 and Greatest Common Factor (GCF) of 2625 and 673 is 1.

  3. Example 3: Find if 7, 15, 35, 125, 175, 375, 405 and 525 are factors of 2625.

    Solution:

    When we divide 2625 by 405 it leaves a remainder. Therefore, the number 405 is not a factor of 2625. All numbers except 405 are factors of 2625.

  4. Example 4: Find the product of all the prime factors of 2625.

    Solution:

    Since, the prime factors of 2625 are 3, 5, 7. Therefore, the product of prime factors = 3 × 5 × 7 = 105.

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FAQs on Factors of 2625

What are the Factors of 2625?

The factors of 2625 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625 and its negative factors are -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -125, -175, -375, -525, -875, -2625.

What is the Sum of all the Factors of 2625?

Sum of all factors of 2625 = (31 + 1 - 1)/(3 - 1) × (53 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 4992

What are the Prime Factors of 2625?

The prime factors of 2625 are 3, 5, 7.

What is the Greatest Common Factor of 2625 and 1095?

The factors of 2625 and 1095 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625 and 1, 3, 5, 15, 73, 219, 365, 1095 respectively.

Common factors of 2625 and 1095 are [1, 3, 5, 15].

Hence, the Greatest Common Factor (GCF) of 2625 and 1095 is 15.

How Many Factors of 648 are also common to the Factors of 2625?

Since, the factors of 2625 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625 and 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.
Hence, [1, 3] are the common factors of 2625 and 648.

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