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Factors of 2475

Factors of 2475 are the list of integers that we can split evenly into 2475. There are overall 18 factors of 2475 among which 2475 is the biggest factor and its prime factors are 3, 5, 11. The Prime Factorization of 2475 is 32 × 52 × 111.

  • All Factors of 2475: 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825 and 2475
  • Prime Factors of 2475: 3, 5, 11
  • Prime Factorization of 2475: 32 × 52 × 111
  • Sum of Factors of 2475: 4836
1. What Are the Factors of 2475?
2. Factors of 2475 by Prime Factorization
3. Factors of 2475 in Pairs
4. FAQs on Factors of 2475
Factors of 2475

What are Factors of 2475?

Factors of 2475 are pairs of those numbers whose products result in 2475. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2475?

To find the factors of 2475, we will have to find the list of numbers that would divide 2475 without leaving any remainder.

  • 2475/55 = 45; therefore, 55 is a factor of 2475 and 45 is also a factor of 2475.
  • 2475/165 = 15; therefore, 165 is a factor of 2475 and 15 is also a factor of 2475.
Similarly we can find other factors. Hence, the factors of 2475 are 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475.

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Factors of 2475 by Prime Factorization

The number 2475 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2475. The first step is to divide the number 2475 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 2475 ÷ 3 = 825
  • 825 ÷ 3 = 275

Further dividing 275 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 275 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 2475 can be written as 32 × 52 × 111 where 3, 5, 11 are prime.

 

Factors of 2475 in Pairs

Pair factors of 2475 are the pairs of numbers that when multiplied give the product 2475. The factors of 2475 in pairs are:

  • 1 × 2475 = (1, 2475)
  • 3 × 825 = (3, 825)
  • 5 × 495 = (5, 495)
  • 9 × 275 = (9, 275)
  • 11 × 225 = (11, 225)
  • 15 × 165 = (15, 165)
  • 25 × 99 = (25, 99)
  • 33 × 75 = (33, 75)
  • 45 × 55 = (45, 55)

Negative pair factors of 2475 are:

  • -1 × -2475 = (-1, -2475)
  • -3 × -825 = (-3, -825)
  • -5 × -495 = (-5, -495)
  • -9 × -275 = (-9, -275)
  • -11 × -225 = (-11, -225)
  • -15 × -165 = (-15, -165)
  • -25 × -99 = (-25, -99)
  • -33 × -75 = (-33, -75)
  • -45 × -55 = (-45, -55)

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

Factors of 2475 Solved Examples

  1. Example 1: How many factors are there for 2475?

    Solution:

    The factors of 2475 are too many, therefore if we can find the prime factorization of 2475, 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 2475 = 32 × 52 × 111
    Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 2475 and 2151.

    Solution:

    The factors of 2475 are 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475 and factors of 2151 are 1, 3, 9, 239, 717, 2151.

    Therefore, the Lowest Common Multiple (LCM) of 2475 and 2151 is 591525 and Highest Common Factor (HCF) of 2475 and 2151 is 9.

  3. Example 3: Find if 1, 55, 99, 225, 275, 825, 2293 and 2475 are factors of 2475.

    Solution:

    When we divide 2475 by 2293 it leaves a remainder. Therefore, the number 2293 is not a factor of 2475. All numbers except 2293 are factors of 2475.

  4. Example 4: Find the product of all the prime factors of 2475.

    Solution:

    Since, the prime factors of 2475 are 3, 5, 11. Therefore, the product of prime factors = 3 × 5 × 11 = 165.

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FAQs on Factors of 2475

What are the Factors of 2475?

The factors of 2475 are 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475 and its negative factors are -1, -3, -5, -9, -11, -15, -25, -33, -45, -55, -75, -99, -165, -225, -275, -495, -825, -2475.

What is the Sum of all the Factors of 2475?

Sum of all factors of 2475 = (32 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 4836

What Numbers are the Prime Factors of 2475?

The prime factors of 2475 are 3, 5, 11.

What is the Greatest Common Factor of 2475 and 626?

The factors of 2475 are 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475 and the factors of 626 are 1, 2, 313, 626. 2475 and 626 have only one common factor which is 1. This implies that 2475 and 626 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2475 and 626 is 1.

What are the Common Factors of 2475 and 1338?

Since, the factors of 2475 are 1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475 and the factors of 1338 are 1, 2, 3, 6, 223, 446, 669, 1338.
Hence, [1, 3] are the common factors of 2475 and 1338.

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