# Factors of 600

Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600

#### How to find factors of a number

 1.   Find factors of 600 using Division Method 2.   Find factors of 600 using Prime Factorization 3.   Find factors of 600 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 600

• Divide 600 by 1: 600 ÷ 1 : Remainder = 0
• Divide 600 by 2: 600 ÷ 2 : Remainder = 0
• Divide 600 by 3: 600 ÷ 3 : Remainder = 0
• Divide 600 by 4: 600 ÷ 4 : Remainder = 0
• Divide 600 by 5: 600 ÷ 5 : Remainder = 0
• Divide 600 by 6: 600 ÷ 6 : Remainder = 0
• Divide 600 by 8: 600 ÷ 8 : Remainder = 0
• Divide 600 by 10: 600 ÷ 10 : Remainder = 0
• Divide 600 by 12: 600 ÷ 12 : Remainder = 0
• Divide 600 by 15: 600 ÷ 15 : Remainder = 0
• Divide 600 by 20: 600 ÷ 20 : Remainder = 0
• Divide 600 by 24: 600 ÷ 24 : Remainder = 0
• Divide 600 by 25: 600 ÷ 25 : Remainder = 0
• Divide 600 by 30: 600 ÷ 30 : Remainder = 0
• Divide 600 by 40: 600 ÷ 40 : Remainder = 0
• Divide 600 by 50: 600 ÷ 50 : Remainder = 0
• Divide 600 by 60: 600 ÷ 60 : Remainder = 0
• Divide 600 by 75: 600 ÷ 75 : Remainder = 0
• Divide 600 by 100: 600 ÷ 100 : Remainder = 0
• Divide 600 by 120: 600 ÷ 120 : Remainder = 0
• Divide 600 by 150: 600 ÷ 150 : Remainder = 0
• Divide 600 by 200: 600 ÷ 200 : Remainder = 0
• Divide 600 by 300: 600 ÷ 300 : Remainder = 0
• Divide 600 by 600: 600 ÷ 600 : Remainder = 0

Hence, Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600

#### 2. Steps to find factors of 600 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 600 using the division method, follow these steps:

• Step 1. Start dividing 600 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 600, which is 2. Divide 600 by 2 to obtain the quotient (300).
600 ÷ 2 = 300
• Step 3. Repeat step 1 with the obtained quotient (300).
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 600 is, 600 = 2 x 2 x 2 x 3 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 600 as shown below:

So, the prime factorization of 600 is, 600 = 2 x 2 x 2 x 3 x 5 x 5.

#### 3. Find factors of 600 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 600 would be the two numbers which, when multiplied, give 600 as the result.

The following table represents the calculation of factors of 600 in pairs:

Factor Pair Pair Factorization
1 and 600 1 x 600 = 600
2 and 300 2 x 300 = 600
3 and 200 3 x 200 = 600
4 and 150 4 x 150 = 600
5 and 120 5 x 120 = 600
6 and 100 6 x 100 = 600
8 and 75 8 x 75 = 600
10 and 60 10 x 60 = 600
12 and 50 12 x 50 = 600
15 and 40 15 x 40 = 600
20 and 30 20 x 30 = 600
24 and 25 24 x 25 = 600

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 600. They are called negative pair factors.

Hence, the negative pairs of 600 would be ( -1 , -600 ) , ( -2 , -300 ) , ( -3 , -200 ) , ( -4 , -150 ) , ( -5 , -120 ) , ( -6 , -100 ) , ( -8 , -75 ) , ( -10 , -60 ) , ( -12 , -50 ) , ( -15 , -40 ) , ( -20 , -30 ) and ( -24 , -25 ) .

#### 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. 600 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 600.
• Every number is a factor of zero (0), since 600 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, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are exact divisors of 600.
• Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600. Each factor divides 600 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600 are all less than or equal to 600.

• How do you find factors of a negative number? ( eg. -600 )?

Factors of -600 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -25, -30, -40, -50, -60, -75, -100, -120, -150, -200, -300, -600.

• What is the sum of all factors of 600?

The sum of all factors of 600 is 1860.

• What is prime factorization of 600?

Prime factorization of 600 is 2 x 2 x 2 x 3 x 5 x 5.

• What are the pair factors of 600?

Pair factors of 600 are (1,600), (2,300), (3,200), (4,150), (5,120), (6,100), (8,75), (10,60), (12,50), (15,40), (20,30), (24,25).

• What are six multiples of 600?

First five multiples of 600 are 1200, 1800, 2400, 3000, 3600, 4200.

• Is 600 a whole number?

Yes 600 is a whole number.

• Which is the smallest prime factor of 600?

Smallest prime factor of 600 is 2.

• What are five multiples of 600?

First five multiples of 600 are 1200, 1800, 2400, 3000, 3600.

• Write all factors of 600?

Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.

#### Examples of Factors

Joey wants to write all the prime factors of 600 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 600 are 2, 2, 2, 3, 5, 5.
So in exponential form it can be written as 23 x 3 x 52.

How many factors are there for 600?

Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 600. Can you predict the answer?

23 factor(s) of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300.

Sammy is puzzled while calculating the prime factors of 600. Can you help him find them?

Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.
Prime factors of 600 are 2, 2, 2, 3, 5, 5

What is prime factorization of 600?

Prime factorization of 600 is 2 x 2 x 2 x 3 x 5 x 5 = 23 x 3 x 52.

Ariel has been assigned the task to find the product of all the prime factors of 600. Can you help her?

Prime factors of 600 are 2, 2, 2, 3, 5, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 600?

Factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.
Even factors of 600 are 2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 50, 60, 100, 120, 150, 200, 300, 600.
Hence, product of even factors of 600 is; 2 x 4 x 6 x 8 x 10 x 12 x 20 x 24 x 30 x 40 x 50 x 60 x 100 x 120 x 150 x 200 x 300 x 600 = 5.159780352e+27.