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Factors of 3750

Factors of 3750 are the list of integers that we can split evenly into 3750. There are 20 factors of 3750 of which 3750 itself is the biggest factor and its prime factors are 2, 3, 5 The Prime Factorization of 3750 is 21 × 31 × 54.

  • All Factors of 3750: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875 and 3750
  • Prime Factors of 3750: 2, 3, 5
  • Prime Factorization of 3750: 21 × 31 × 54
  • Sum of Factors of 3750: 9372
1. What Are the Factors of 3750?
2. Factors of 3750 by Prime Factorization
3. Factors of 3750 in Pairs
4. FAQs on Factors of 3750
Factors of 3750

What are Factors of 3750?

Factors of 3750 are pairs of those numbers whose products result in 3750. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3750?

To find the factors of 3750, we will have to find the list of numbers that would divide 3750 without leaving any remainder.

  • 3750/3750 = 1; therefore, 3750 is a factor of 3750.
  • 3750/125 = 30; therefore, 125 is a factor of 3750.
Similarly we can find other factors. Hence, the factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750.

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Factors of 3750 by Prime Factorization

The number 3750 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3750. The first step is to divide the number 3750 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 3750 ÷ 2 = 1875

Further dividing 1875 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1875 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 3750 can be written as 21 × 31 × 54 where 2, 3, 5 are prime.

 

Factors of 3750 in Pairs

Pair factors of 3750 are the pairs of numbers that when multiplied give the product 3750. The factors of 3750 in pairs are:

  • 1 × 3750 = (1, 3750)
  • 2 × 1875 = (2, 1875)
  • 3 × 1250 = (3, 1250)
  • 5 × 750 = (5, 750)
  • 6 × 625 = (6, 625)
  • 10 × 375 = (10, 375)
  • 15 × 250 = (15, 250)
  • 25 × 150 = (25, 150)
  • 30 × 125 = (30, 125)
  • 50 × 75 = (50, 75)

Negative pair factors of 3750 are:

  • -1 × -3750 = (-1, -3750)
  • -2 × -1875 = (-2, -1875)
  • -3 × -1250 = (-3, -1250)
  • -5 × -750 = (-5, -750)
  • -6 × -625 = (-6, -625)
  • -10 × -375 = (-10, -375)
  • -15 × -250 = (-15, -250)
  • -25 × -150 = (-25, -150)
  • -30 × -125 = (-30, -125)
  • -50 × -75 = (-50, -75)

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

Factors of 3750 Solved Examples

  1. Example 1: How many factors are there for 3750?

    Solution:

    The factors of 3750 are too many, therefore if we can find the prime factorization of 3750, 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 3750 = 21 × 31 × 54
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (4 + 1) = 2 × 2 × 5 = 20

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 3750 and 652.

    Solution:

    The factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750 and factors of 652 are 1, 2, 4, 163, 326, 652.

    Therefore, the Lowest Common Multiple (LCM) of 3750 and 652 is 1222500 and Highest Common Factor (HCF) of 3750 and 652 is 2.

  3. Example 3: Find if 3, 10, 50, 125, 150, 250, 375 and 3204 are factors of 3750.

    Solution:

    When we divide 3750 by 3204 it leaves a remainder. Therefore, the number 3204 is not a factor of 3750. All numbers except 3204 are factors of 3750.

  4. Example 4: Find the product of all the prime factors of 3750.

    Solution:

    Since, the prime factors of 3750 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 3750

What are the Factors of 3750?

The factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750 and its negative factors are -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75, -125, -150, -250, -375, -625, -750, -1250, -1875, -3750.

What is the Sum of the Factors of 3750?

Sum of all factors of 3750 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (54 + 1 - 1)/(5 - 1) = 9372

What are Prime Factors of 3750?

The prime factors of 3750 are 2, 3, 5.

What is the Greatest Common Factor of 3750 and 2970?

The factors of 3750 and 2970 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750 and 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 90, 99, 110, 135, 165, 198, 270, 297, 330, 495, 594, 990, 1485, 2970 respectively.

Common factors of 3750 and 2970 are [1, 2, 3, 5, 6, 10, 15, 30].

Hence, the GCF of 3750 and 2970 is 30.

How Many Factors of 3750 are also common to the Factors of 3296?

Since, the factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750 and the factors of 3296 are 1, 2, 4, 8, 16, 32, 103, 206, 412, 824, 1648, 3296.
Hence, [1, 2] are the common factors of 3750 and 3296.

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