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Factors of 2145

Factors of 2145 are numbers that, when multiplied in pairs give the product as 2145. There are 16 factors of 2145, of which the following are its prime factors 3, 5, 11, 13. The Prime Factorization of 2145 is 31 × 51 × 111 × 131.

  • All Factors of 2145: 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715 and 2145
  • Prime Factors of 2145: 3, 5, 11, 13
  • Prime Factorization of 2145: 31 × 51 × 111 × 131
  • Sum of Factors of 2145: 4032
1. What Are the Factors of 2145?
2. Factors of 2145 by Prime Factorization
3. Factors of 2145 in Pairs
4. FAQs on Factors of 2145
Factors of 2145

What are Factors of 2145?

Factors of 2145 are pairs of those numbers whose products result in 2145. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2145?

To find the factors of 2145, we will have to find the list of numbers that would divide 2145 without leaving any remainder.

  • 2145/13 = 165; therefore, 13 is a factor of 2145 and 165 is also a factor of 2145.
  • 2145/15 = 143; therefore, 15 is a factor of 2145 and 143 is also a factor of 2145.
Similarly we can find other factors. Hence, the factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145.

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Factors of 2145 by Prime Factorization

The number 2145 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2145. The first step is to divide the number 2145 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 2145 ÷ 3 = 715

Further dividing 715 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 715 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 2145 can be written as 31 × 51 × 111 × 131 where 3, 5, 11, 13 are prime.

 

Factors of 2145 in Pairs

Pair factors of 2145 are the pairs of numbers that when multiplied give the product 2145. The factors of 2145 in pairs are:

  • 1 × 2145 = (1, 2145)
  • 3 × 715 = (3, 715)
  • 5 × 429 = (5, 429)
  • 11 × 195 = (11, 195)
  • 13 × 165 = (13, 165)
  • 15 × 143 = (15, 143)
  • 33 × 65 = (33, 65)
  • 39 × 55 = (39, 55)

Negative pair factors of 2145 are:

  • -1 × -2145 = (-1, -2145)
  • -3 × -715 = (-3, -715)
  • -5 × -429 = (-5, -429)
  • -11 × -195 = (-11, -195)
  • -13 × -165 = (-13, -165)
  • -15 × -143 = (-15, -143)
  • -33 × -65 = (-33, -65)
  • -39 × -55 = (-39, -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 2145 Solved Examples

  1. Example 1: How many factors are there for 2145?

    Solution:

    The factors of 2145 are too many, therefore if we can find the prime factorization of 2145, 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 2145 = 31 × 51 × 111 × 131
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 2145 and 1375.

    Solution:

    The factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145 and factors of 1375 are 1, 5, 11, 25, 55, 125, 275, 1375.

    Therefore, the Least Common Multiple (LCM) of 2145 and 1375 is 53625 and Highest Common Factor (HCF) of 2145 and 1375 is 55.

  3. Example 3: Find if 1, 3, 5, 55, 143, 195, 1470 and 2145 are factors of 2145.

    Solution:

    When we divide 2145 by 1470 it leaves a remainder. Therefore, the number 1470 is not a factor of 2145. All numbers except 1470 are factors of 2145.

  4. Example 4: Find the product of all the prime factors of 2145.

    Solution:

    Since, the prime factors of 2145 are 3, 5, 11, 13. Therefore, the product of prime factors = 3 × 5 × 11 × 13 = 2145.

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FAQs on Factors of 2145

What are the Factors of 2145?

The factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145 and its negative factors are -1, -3, -5, -11, -13, -15, -33, -39, -55, -65, -143, -165, -195, -429, -715, -2145.

What is the Sum of all the Factors of 2145?

Sum of all factors of 2145 = (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) × (131 + 1 - 1)/(13 - 1) = 4032

What are Pair Factors of 2145?

The pair factors of 2145 are (1, 2145), (3, 715), (5, 429), (11, 195), (13, 165), (15, 143), (33, 65), (39, 55).

What is the Greatest Common Factor of 2145 and 1495?

The factors of 2145 and 1495 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145 and 1, 5, 13, 23, 65, 115, 299, 1495 respectively.

Common factors of 2145 and 1495 are [1, 5, 13, 65].

Hence, the GCF of 2145 and 1495 is 65.

How Many Factors of 2145 are also Factors of 1976?

Since, the factors of 2145 are 1, 3, 5, 11, 13, 15, 33, 39, 55, 65, 143, 165, 195, 429, 715, 2145 and the factors of 1976 are 1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988, 1976.
Hence, [1, 13] are the common factors of 2145 and 1976.

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