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Factors of 1755

Factors of 1755 are the list of integers that we can split evenly into 1755. It has total 16 factors of which 1755 is the biggest factor and the prime factors of 1755 are 3, 5, 13. The Prime Factorization of 1755 is 33 × 51 × 131.

  • All Factors of 1755: 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585 and 1755
  • Prime Factors of 1755: 3, 5, 13
  • Prime Factorization of 1755: 33 × 51 × 131
  • Sum of Factors of 1755: 3360
1. What Are the Factors of 1755?
2. Factors of 1755 by Prime Factorization
3. Factors of 1755 in Pairs
4. FAQs on Factors of 1755
Factors of 1755

What are Factors of 1755?

Factors of 1755 are pairs of those numbers whose products result in 1755. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1755?

To find the factors of 1755, we will have to find the list of numbers that would divide 1755 without leaving any remainder.

  • 1755/117 = 15; therefore, 117 is a factor of 1755 and 15 is also a factor of 1755.
  • 1755/9 = 195; therefore, 9 is a factor of 1755 and 195 is also a factor of 1755.
Similarly we can find other factors. Hence, the factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755.

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Factors of 1755 by Prime Factorization

The number 1755 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1755. The first step is to divide the number 1755 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1755 ÷ 3 = 585
  • 585 ÷ 3 = 195
  • 195 ÷ 3 = 65

Further dividing 65 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 65 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 1755 can be written as 33 × 51 × 131 where 3, 5, 13 are prime.

 

Factors of 1755 in Pairs

Pair factors of 1755 are the pairs of numbers that when multiplied give the product 1755. The factors of 1755 in pairs are:

  • 1 × 1755 = (1, 1755)
  • 3 × 585 = (3, 585)
  • 5 × 351 = (5, 351)
  • 9 × 195 = (9, 195)
  • 13 × 135 = (13, 135)
  • 15 × 117 = (15, 117)
  • 27 × 65 = (27, 65)
  • 39 × 45 = (39, 45)

Negative pair factors of 1755 are:

  • -1 × -1755 = (-1, -1755)
  • -3 × -585 = (-3, -585)
  • -5 × -351 = (-5, -351)
  • -9 × -195 = (-9, -195)
  • -13 × -135 = (-13, -135)
  • -15 × -117 = (-15, -117)
  • -27 × -65 = (-27, -65)
  • -39 × -45 = (-39, -45)

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

Factors of 1755 Solved Examples

  1. Example 1: How many factors are there for 1755?

    Solution:

    The factors of 1755 are too many, therefore if we can find the prime factorization of 1755, 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 1755 = 33 × 51 × 131
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1755 and 1654.

    Solution:

    The factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755 and factors of 1654 are 1, 2, 827, 1654.

    Therefore, the Least Common Multiple (LCM) of 1755 and 1654 is 2902770 and Greatest Common Divisor (GCD) of 1755 and 1654 is 1.

  3. Example 3: Find if 3, 9, 13, 15, 65, 195, 585 and 769 are factors of 1755.

    Solution:

    When we divide 1755 by 769 it leaves a remainder. Therefore, the number 769 is not a factor of 1755. All numbers except 769 are factors of 1755.

  4. Example 4: Find the product of all the prime factors of 1755.

    Solution:

    Since, the prime factors of 1755 are 3, 5, 13. Therefore, the product of prime factors = 3 × 5 × 13 = 195.

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FAQs on Factors of 1755

What are the Factors of 1755?

The factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755 and its negative factors are -1, -3, -5, -9, -13, -15, -27, -39, -45, -65, -117, -135, -195, -351, -585, -1755.

What is the Sum of all the Factors of 1755?

Sum of all factors of 1755 = (33 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 3360

What are the Pair Factors of 1755?

The pair factors of 1755 are (1, 1755), (3, 585), (5, 351), (9, 195), (13, 135), (15, 117), (27, 65), (39, 45).

What is the Greatest Common Factor of 1755 and 969?

The factors of 1755 and 969 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755 and 1, 3, 17, 19, 51, 57, 323, 969 respectively.

Common factors of 1755 and 969 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 1755 and 969 is 3.

How Many Factors of 1755 are also Factors of 500?

Since, the factors of 1755 are 1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 117, 135, 195, 351, 585, 1755 and the factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.
Hence, [1, 5] are the common factors of 1755 and 500.

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