1. Steps to find factors of 3750 using Division Method

Example: Find factors of 3750

  • Divide 3750 by 1: 3750 ÷ 1 : Remainder = 0
  • Divide 3750 by 2: 3750 ÷ 2 : Remainder = 0
  • Divide 3750 by 3: 3750 ÷ 3 : Remainder = 0
  • Divide 3750 by 5: 3750 ÷ 5 : Remainder = 0
  • Divide 3750 by 6: 3750 ÷ 6 : Remainder = 0
  • Divide 3750 by 10: 3750 ÷ 10 : Remainder = 0
  • Divide 3750 by 15: 3750 ÷ 15 : Remainder = 0
  • Divide 3750 by 25: 3750 ÷ 25 : Remainder = 0
  • Divide 3750 by 30: 3750 ÷ 30 : Remainder = 0
  • Divide 3750 by 50: 3750 ÷ 50 : Remainder = 0
  • Divide 3750 by 75: 3750 ÷ 75 : Remainder = 0
  • Divide 3750 by 125: 3750 ÷ 125 : Remainder = 0
  • Divide 3750 by 150: 3750 ÷ 150 : Remainder = 0
  • Divide 3750 by 250: 3750 ÷ 250 : Remainder = 0
  • Divide 3750 by 375: 3750 ÷ 375 : Remainder = 0
  • Divide 3750 by 625: 3750 ÷ 625 : Remainder = 0
  • Divide 3750 by 750: 3750 ÷ 750 : Remainder = 0
  • Divide 3750 by 1250: 3750 ÷ 1250 : Remainder = 0
  • Divide 3750 by 1875: 3750 ÷ 1875 : Remainder = 0
  • Divide 3750 by 3750: 3750 ÷ 3750 : Remainder = 0

Hence, Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, and 3750

2. Steps to find factors of 3750 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 3750 using the division method, follow these steps:

  • Step 1. Start dividing 3750 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 3750, which is 2. Divide 3750 by 2 to obtain the quotient (1875).
    3750 ÷ 2 = 1875
  • Step 3. Repeat step 1 with the obtained quotient (1875).
    1875 ÷ 3 = 625
    625 ÷ 5 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 3750 is, 3750 = 2 x 3 x 5 x 5 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3750 as shown below:

So, the prime factorization of 3750 is, 3750 = 2 x 3 x 5 x 5 x 5 x 5.

3. Find factors of 3750 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 3750 would be the two numbers which, when multiplied, give 3750 as the result.

The following table represents the calculation of factors of 3750 in pairs:

Factor Pair Pair Factorization
1 and 3750 1 x 3750 = 3750
2 and 1875 2 x 1875 = 3750
3 and 1250 3 x 1250 = 3750
5 and 750 5 x 750 = 3750
6 and 625 6 x 625 = 3750
10 and 375 10 x 375 = 3750
15 and 250 15 x 250 = 3750
25 and 150 25 x 150 = 3750
30 and 125 30 x 125 = 3750
50 and 75 50 x 75 = 3750

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 3750. They are called negative pair factors.

Hence, the negative pairs of 3750 would be ( -1 , -3750 ) , ( -2 , -1875 ) , ( -3 , -1250 ) , ( -5 , -750 ) , ( -6 , -625 ) , ( -10 , -375 ) , ( -15 , -250 ) , ( -25 , -150 ) , ( -30 , -125 ) and ( -50 , -75 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 3750 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750 are exact divisors of 3750.
  • 1 is a factor of every number. Eg. 1 is a factor of 3750.
  • Every number is a factor of zero (0), since 3750 x 0 = 0.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -3750 )?

    Factors of -3750 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 all factors of 3750?

    The sum of all factors of 3750 is 9372.

  • What is prime factorization of 3750?

    Prime factorization of 3750 is 2 x 3 x 5 x 5 x 5 x 5.

  • What are the pair factors of 3750?

    Pair factors of 3750 are (1,3750), (2,1875), (3,1250), (5,750), (6,625), (10,375), (15,250), (25,150), (30,125), (50,75).

  • What are six multiples of 3750?

    First five multiples of 3750 are 7500, 11250, 15000, 18750, 22500, 26250.

  • Is 3750 a whole number?

    Yes 3750 is a whole number.

  • Which is the smallest prime factor of 3750?

    Smallest prime factor of 3750 is 2.

  • What are five multiples of 3750?

    First five multiples of 3750 are 7500, 11250, 15000, 18750, 22500.

  • Write all factors of 3750?

    Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750.

Examples of Factors

Joey wants to write all the prime factors of 3750 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3750 are 2, 3, 5, 5, 5, 5.
So in exponential form it can be written as 2 x 3 x 54.

How many factors are there for 3750?

Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750.
So there are in total 20 factors.

Kevin has been asked to write 19 factor(s) of 3750. Can you predict the answer?

19 factor(s) of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875.

Sammy is puzzled while calculating the prime factors of 3750. Can you help him find them?

Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750.
Prime factors of 3750 are 2, 3, 5, 5, 5, 5

What is prime factorization of 3750?

Prime factorization of 3750 is 2 x 3 x 5 x 5 x 5 x 5 = 2 x 3 x 54.

Ariel has been assigned the task to find the product of all the prime factors of 3750. Can you help her?

Prime factors of 3750 are 2, 3, 5, 5, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 3750?

Factors of 3750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 625, 750, 1250, 1875, 3750.
Even factors of 3750 are 2, 6, 10, 30, 50, 150, 250, 750, 1250, 3750.
Hence, product of even factors of 3750 is; 2 x 6 x 10 x 30 x 50 x 150 x 250 x 750 x 1250 x 3750 = 23730468750000000000.