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Factors of 3675

Factors of 3675 are numbers that, when multiplied in pairs give the product as 3675. There are total 18 factors of 3675, of which 3, 5, 7 are its prime factors. The sum of all factors of 3675 is 7068.

  • All Factors of 3675: 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225 and 3675
  • Prime Factors of 3675: 3, 5, 7
  • Prime Factorization of 3675: 31 × 52 × 72
  • Sum of Factors of 3675: 7068
1. What Are the Factors of 3675?
2. Factors of 3675 by Prime Factorization
3. Factors of 3675 in Pairs
4. FAQs on Factors of 3675
Factors of 3675

What are Factors of 3675?

Factors of 3675 are pairs of those numbers whose products result in 3675. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3675?

To find the factors of 3675, we will have to find the list of numbers that would divide 3675 without leaving any remainder.

  • 3675/21 = 175; therefore, 21 is a factor of 3675 and 175 is also a factor of 3675.
  • 3675/3 = 1225; therefore, 3 is a factor of 3675 and 1225 is also a factor of 3675.
Similarly we can find other factors. Hence, the factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675.

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Factors of 3675 by Prime Factorization

The number 3675 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3675. The first step is to divide the number 3675 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 3675 ÷ 3 = 1225

Further dividing 1225 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 1225 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 3675 can be written as 31 × 52 × 72 where 3, 5, 7 are prime.

 

Factors of 3675 in Pairs

Pair factors of 3675 are the pairs of numbers that when multiplied give the product 3675. The factors of 3675 in pairs are:

  • 1 × 3675 = (1, 3675)
  • 3 × 1225 = (3, 1225)
  • 5 × 735 = (5, 735)
  • 7 × 525 = (7, 525)
  • 15 × 245 = (15, 245)
  • 21 × 175 = (21, 175)
  • 25 × 147 = (25, 147)
  • 35 × 105 = (35, 105)
  • 49 × 75 = (49, 75)

Negative pair factors of 3675 are:

  • -1 × -3675 = (-1, -3675)
  • -3 × -1225 = (-3, -1225)
  • -5 × -735 = (-5, -735)
  • -7 × -525 = (-7, -525)
  • -15 × -245 = (-15, -245)
  • -21 × -175 = (-21, -175)
  • -25 × -147 = (-25, -147)
  • -35 × -105 = (-35, -105)
  • -49 × -75 = (-49, -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 3675 Solved Examples

  1. Example 1: How many factors are there for 3675?

    Solution:

    The factors of 3675 are too many, therefore if we can find the prime factorization of 3675, 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 3675 = 31 × 52 × 72
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (2 + 1) = 2 × 3 × 3 = 18

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 3675 and 446.

    Solution:

    The factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675 and factors of 446 are 1, 2, 223, 446.

    Therefore, the Least Common Multiple (LCM) of 3675 and 446 is 1639050 and Greatest Common Divisor (GCD) of 3675 and 446 is 1.

  3. Example 3: Find if 3, 7, 21, 35, 75, 274, 525 and 3675 are factors of 3675.

    Solution:

    When we divide 3675 by 274 it leaves a remainder. Therefore, the number 274 is not a factor of 3675. All numbers except 274 are factors of 3675.

  4. Example 4: Find the product of all the prime factors of 3675.

    Solution:

    Since, the prime factors of 3675 are 3, 5, 7. Therefore, the product of prime factors = 3 × 5 × 7 = 105.

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FAQs on Factors of 3675

What are the Factors of 3675?

The factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675 and its negative factors are -1, -3, -5, -7, -15, -21, -25, -35, -49, -75, -105, -147, -175, -245, -525, -735, -1225, -3675.

What is the Sum of the Factors of 3675?

Sum of all factors of 3675 = (31 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) × (72 + 1 - 1)/(7 - 1) = 7068

What Numbers are the Prime Factors of 3675?

The prime factors of 3675 are 3, 5, 7.

What is the Greatest Common Factor of 3675 and 2574?

The factors of 3675 and 2574 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675 and 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 198, 234, 286, 429, 858, 1287, 2574 respectively.

Common factors of 3675 and 2574 are [1, 3].

Hence, the Greatest Common Factor of 3675 and 2574 is 3.

What are the Common Factors of 3675 and 1173?

Since, the factors of 3675 are 1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675 and the factors of 1173 are 1, 3, 17, 23, 51, 69, 391, 1173.
Hence, [1, 3] are the common factors of 3675 and 1173.

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