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Factors of 1750

Factors of 1750 are the list of integers that we can split evenly into 1750. There are overall 16 factors of 1750 among which 1750 is the biggest factor and 2, 5, 7 are its prime factors. The Prime Factorization of 1750 is 21 × 53 × 71.

  • All Factors of 1750: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875 and 1750
  • Prime Factors of 1750: 2, 5, 7
  • Prime Factorization of 1750: 21 × 53 × 71
  • Sum of Factors of 1750: 3744
1. What Are the Factors of 1750?
2. Factors of 1750 by Prime Factorization
3. Factors of 1750 in Pairs
4. FAQs on Factors of 1750
Factors of 1750

What are Factors of 1750?

Factors of 1750 are pairs of those numbers whose products result in 1750. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1750?

To find the factors of 1750, we will have to find the list of numbers that would divide 1750 without leaving any remainder.

  • 1750/1 = 1750; therefore, 1 is a factor of 1750.
  • 1750/25 = 70; therefore, 25 is a factor of 1750.
Similarly we can find other factors. Hence, the factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.

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Factors of 1750 by Prime Factorization

The number 1750 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1750. The first step is to divide the number 1750 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1750 ÷ 2 = 875

Further dividing 875 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 875 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 1750 can be written as 21 × 53 × 71 where 2, 5, 7 are prime.

 

Factors of 1750 in Pairs

Pair factors of 1750 are the pairs of numbers that when multiplied give the product 1750. The factors of 1750 in pairs are:

  • 1 × 1750 = (1, 1750)
  • 2 × 875 = (2, 875)
  • 5 × 350 = (5, 350)
  • 7 × 250 = (7, 250)
  • 10 × 175 = (10, 175)
  • 14 × 125 = (14, 125)
  • 25 × 70 = (25, 70)
  • 35 × 50 = (35, 50)

Negative pair factors of 1750 are:

  • -1 × -1750 = (-1, -1750)
  • -2 × -875 = (-2, -875)
  • -5 × -350 = (-5, -350)
  • -7 × -250 = (-7, -250)
  • -10 × -175 = (-10, -175)
  • -14 × -125 = (-14, -125)
  • -25 × -70 = (-25, -70)
  • -35 × -50 = (-35, -50)

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

Factors of 1750 Solved Examples

  1. Example 1: How many factors are there for 1750?

    Solution:

    The factors of 1750 are too many, therefore if we can find the prime factorization of 1750, 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 1750 = 21 × 53 × 71
    Therefore, the total number of factors are (1 + 1) × (3 + 1) × (1 + 1) = 2 × 4 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1750 and 437.

    Solution:

    The factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750 and factors of 437 are 1, 19, 23, 437.

    Therefore, the Lowest Common Multiple (LCM) of 1750 and 437 is 764750 and Greatest Common Divisor (GCD) of 1750 and 437 is 1.

  3. Example 3: Find if 2, 7, 25, 35, 175, 450, 875 and 1750 are factors of 1750.

    Solution:

    When we divide 1750 by 450 it leaves a remainder. Therefore, the number 450 is not a factor of 1750. All numbers except 450 are factors of 1750.

  4. Example 4: Find the product of all the prime factors of 1750.

    Solution:

    Since, the prime factors of 1750 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 1750

What are the Factors of 1750?

The factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750 and its negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -125, -175, -250, -350, -875, -1750.

What is the Sum of all Factors of 1750?

Sum of all factors of 1750 = (21 + 1 - 1)/(2 - 1) × (53 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 3744

What numbers are the Pair Factors of 1750?

The pair factors of 1750 are (1, 1750), (2, 875), (5, 350), (7, 250), (10, 175), (14, 125), (25, 70), (35, 50).

What is the Greatest Common Factor of 1750 and 1436?

The factors of 1750 and 1436 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750 and 1, 2, 4, 359, 718, 1436 respectively.

Common factors of 1750 and 1436 are [1, 2].

Hence, the GCF of 1750 and 1436 is 2.

What are the Common Factors of 1750 and 1393?

Since, the factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750 and the factors of 1393 are 1, 7, 199, 1393.
Hence, [1, 7] are the common factors of 1750 and 1393.

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