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Factors of 2541

Factors of 2541 are the list of integers that we can split evenly into 2541. There are overall 12 factors of 2541 among which 2541 is the biggest factor and its prime factors are 3, 7, 11. The sum of all factors of 2541 is 4256.

  • All Factors of 2541: 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847 and 2541
  • Prime Factors of 2541: 3, 7, 11
  • Prime Factorization of 2541: 31 × 71 × 112
  • Sum of Factors of 2541: 4256
1. What Are the Factors of 2541?
2. Factors of 2541 by Prime Factorization
3. Factors of 2541 in Pairs
4. FAQs on Factors of 2541
Factors of 2541

What are Factors of 2541?

Factors of 2541 are pairs of those numbers whose products result in 2541. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2541?

To find the factors of 2541, we will have to find the list of numbers that would divide 2541 without leaving any remainder.

  • 2541/121 = 21; therefore, 121 is a factor of 2541 and 21 is also a factor of 2541.
  • 2541/33 = 77; therefore, 33 is a factor of 2541 and 77 is also a factor of 2541.
Similarly we can find other factors. Hence, the factors of 2541 are 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541.

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Factors of 2541 by Prime Factorization

The number 2541 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2541. The first step is to divide the number 2541 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 2541 ÷ 3 = 847

Further dividing 847 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 847 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 2541 can be written as 31 × 71 × 112 where 3, 7, 11 are prime.

 

Factors of 2541 in Pairs

Pair factors of 2541 are the pairs of numbers that when multiplied give the product 2541. The factors of 2541 in pairs are:

  • 1 × 2541 = (1, 2541)
  • 3 × 847 = (3, 847)
  • 7 × 363 = (7, 363)
  • 11 × 231 = (11, 231)
  • 21 × 121 = (21, 121)
  • 33 × 77 = (33, 77)

Negative pair factors of 2541 are:

  • -1 × -2541 = (-1, -2541)
  • -3 × -847 = (-3, -847)
  • -7 × -363 = (-7, -363)
  • -11 × -231 = (-11, -231)
  • -21 × -121 = (-21, -121)
  • -33 × -77 = (-33, -77)

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

Factors of 2541 Solved Examples

  1. Example 1: How many factors are there for 2541?

    Solution:

    The factors of 2541 are too many, therefore if we can find the prime factorization of 2541, 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 2541 = 31 × 71 × 112
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 3 = 12

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 2541 and 42.

    Solution:

    The factors of 2541 are 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541 and factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

    Therefore, the LCM of 2541 and 42 is 5082 and Greatest Common Divisor (GCD) of 2541 and 42 is 21.

  3. Example 3: Find if 1, 11, 21, 33, 121, 1329 and 2541 are factors of 2541.

    Solution:

    When we divide 2541 by 1329 it leaves a remainder. Therefore, the number 1329 is not a factor of 2541. All numbers except 1329 are factors of 2541.

  4. Example 4: Find the product of all the prime factors of 2541.

    Solution:

    Since, the prime factors of 2541 are 3, 7, 11. Therefore, the product of prime factors = 3 × 7 × 11 = 231.

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FAQs on Factors of 2541

What are the Factors of 2541?

The factors of 2541 are 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541 and its negative factors are -1, -3, -7, -11, -21, -33, -77, -121, -231, -363, -847, -2541.

What is the Sum of the Factors of 2541?

Sum of all factors of 2541 = (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (112 + 1 - 1)/(11 - 1) = 4256

What are the Prime Factors of 2541?

The prime factors of 2541 are 3, 7, 11.

What is the Greatest Common Factor of 2541 and 1259?

The factors of 2541 are 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541 and the factors of 1259 are 1, 1259. 2541 and 1259 have only one common factor which is 1. This implies that 2541 and 1259 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2541 and 1259 is 1.

How Many Factors of 2541 are also common to the Factors of 438?

Since, the factors of 2541 are 1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541 and the factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438.
Hence, [1, 3] are the common factors of 2541 and 438.

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