# Factors of 1500

Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500

#### How to find factors of a number

 1.   Find factors of 1500 using Division Method 2.   Find factors of 1500 using Prime Factorization 3.   Find factors of 1500 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1500

• Divide 1500 by 1: 1500 ÷ 1 : Remainder = 0
• Divide 1500 by 2: 1500 ÷ 2 : Remainder = 0
• Divide 1500 by 3: 1500 ÷ 3 : Remainder = 0
• Divide 1500 by 4: 1500 ÷ 4 : Remainder = 0
• Divide 1500 by 5: 1500 ÷ 5 : Remainder = 0
• Divide 1500 by 6: 1500 ÷ 6 : Remainder = 0
• Divide 1500 by 10: 1500 ÷ 10 : Remainder = 0
• Divide 1500 by 12: 1500 ÷ 12 : Remainder = 0
• Divide 1500 by 15: 1500 ÷ 15 : Remainder = 0
• Divide 1500 by 20: 1500 ÷ 20 : Remainder = 0
• Divide 1500 by 25: 1500 ÷ 25 : Remainder = 0
• Divide 1500 by 30: 1500 ÷ 30 : Remainder = 0
• Divide 1500 by 50: 1500 ÷ 50 : Remainder = 0
• Divide 1500 by 60: 1500 ÷ 60 : Remainder = 0
• Divide 1500 by 75: 1500 ÷ 75 : Remainder = 0
• Divide 1500 by 100: 1500 ÷ 100 : Remainder = 0
• Divide 1500 by 125: 1500 ÷ 125 : Remainder = 0
• Divide 1500 by 150: 1500 ÷ 150 : Remainder = 0
• Divide 1500 by 250: 1500 ÷ 250 : Remainder = 0
• Divide 1500 by 300: 1500 ÷ 300 : Remainder = 0
• Divide 1500 by 375: 1500 ÷ 375 : Remainder = 0
• Divide 1500 by 500: 1500 ÷ 500 : Remainder = 0
• Divide 1500 by 750: 1500 ÷ 750 : Remainder = 0
• Divide 1500 by 1500: 1500 ÷ 1500 : Remainder = 0

Hence, Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500

#### 2. Steps to find factors of 1500 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 1500 using the division method, follow these steps:

• Step 1. Start dividing 1500 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 1500, which is 2. Divide 1500 by 2 to obtain the quotient (750).
1500 ÷ 2 = 750
• Step 3. Repeat step 1 with the obtained quotient (750).
750 ÷ 2 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 1500 is, 1500 = 2 x 2 x 3 x 5 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1500 as shown below:

So, the prime factorization of 1500 is, 1500 = 2 x 2 x 3 x 5 x 5 x 5.

#### 3. Find factors of 1500 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 1500 would be the two numbers which, when multiplied, give 1500 as the result.

The following table represents the calculation of factors of 1500 in pairs:

Factor Pair Pair Factorization
1 and 1500 1 x 1500 = 1500
2 and 750 2 x 750 = 1500
3 and 500 3 x 500 = 1500
4 and 375 4 x 375 = 1500
5 and 300 5 x 300 = 1500
6 and 250 6 x 250 = 1500
10 and 150 10 x 150 = 1500
12 and 125 12 x 125 = 1500
15 and 100 15 x 100 = 1500
20 and 75 20 x 75 = 1500
25 and 60 25 x 60 = 1500
30 and 50 30 x 50 = 1500

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 1500. They are called negative pair factors.

Hence, the negative pairs of 1500 would be ( -1 , -1500 ) , ( -2 , -750 ) , ( -3 , -500 ) , ( -4 , -375 ) , ( -5 , -300 ) , ( -6 , -250 ) , ( -10 , -150 ) , ( -12 , -125 ) , ( -15 , -100 ) , ( -20 , -75 ) , ( -25 , -60 ) and ( -30 , -50 ) .

#### 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. 1500 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1500.
• Every number is a factor of zero (0), since 1500 x 0 = 0.
• 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, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500 are exact divisors of 1500.
• Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500. Each factor divides 1500 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500 are all less than or equal to 1500.

• How do you find factors of a negative number? ( eg. -1500 )?

Factors of -1500 are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, -1500.

• What is the sum of all factors of 1500?

The sum of all factors of 1500 is 4368.

• What is prime factorization of 1500?

Prime factorization of 1500 is 2 x 2 x 3 x 5 x 5 x 5.

• What are the pair factors of 1500?

Pair factors of 1500 are (1,1500), (2,750), (3,500), (4,375), (5,300), (6,250), (10,150), (12,125), (15,100), (20,75), (25,60), (30,50).

• What are six multiples of 1500?

First five multiples of 1500 are 3000, 4500, 6000, 7500, 9000, 10500.

• Is 1500 a whole number?

Yes 1500 is a whole number.

• Which is the smallest prime factor of 1500?

Smallest prime factor of 1500 is 2.

• What are five multiples of 1500?

First five multiples of 1500 are 3000, 4500, 6000, 7500, 9000.

• Write all factors of 1500?

Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500.

#### Examples of Factors

Joey wants to write all the prime factors of 1500 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1500 are 2, 2, 3, 5, 5, 5.
So in exponential form it can be written as 22 x 3 x 53.

How many factors are there for 1500?

Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1500. Can you predict the answer?

23 factor(s) of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750.

Sammy is puzzled while calculating the prime factors of 1500. Can you help him find them?

Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500.
Prime factors of 1500 are 2, 2, 3, 5, 5, 5

What is prime factorization of 1500?

Prime factorization of 1500 is 2 x 2 x 3 x 5 x 5 x 5 = 22 x 3 x 53.

Ariel has been assigned the task to find the product of all the prime factors of 1500. Can you help her?

Prime factors of 1500 are 2, 2, 3, 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 1500?

Factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500.
Even factors of 1500 are 2, 4, 6, 10, 12, 20, 30, 50, 60, 100, 150, 250, 300, 500, 750, 1500.
Hence, product of even factors of 1500 is; 2 x 4 x 6 x 10 x 12 x 20 x 30 x 50 x 60 x 100 x 150 x 250 x 300 x 500 x 750 x 1500 = 6.561e+27.