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Factors of 600

Did you know that 600 is an even composite number having 24 divisors constituting of the first three prime numbers 2, 3, and 5? In this chapter, we will calculate the factors of 600, prime factors of 600, and factors of 600 in pairs along with solved examples for a better understanding.

Factors of 600: 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
Prime Factorization of 600: 600 = 2 × 2 × 2 × 3 × 5 × 5 = 2³ × 3 × 5²

1.	What Are the Factors of 600?
2.	How to Calculate the Factors of 600?
3.	Factors of 600 by Prime Factorization
4.	Factors of 600 in Pairs
5.	FAQs on Factors of 600

What Are the Factors of 600?

Factors of 600 are the numbers which on multiplication give the product as 600. The factors of 600 are the numbers that divide it without leaving any remainder. So, when any two whole numbers are multiplied with each other and 600 is obtained as the answer, it is said that both these numbers are the factors of 600.

How to Calculate the Factors of 600?

We calculate the factors of 600 by finding all the numbers which would divide 600 without leaving any remainder. 600 can be expressed as a product of its prime factors in the prime factorization method, and we divide 600 with its divisors in the division method. Hence, the divisors, as well as their quotients, are the factors of 600.

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

Hence, the 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.

Explore factors using illustrations and interactive examples.

Factors of 300 - The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Factors of 150 - The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, and 75.
Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, and 50.
Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 600 by Prime Factorization

Prime factorization is referred to as expressing a composite number as the product of its prime factors. To get the prime factorization of 600, we can use two methods:

Method 1: Factor Tree Method
Method 2: Upside-Down Division Method

Method 1: Factor Tree Method

The factor tree of 600 is:

Factor Tree of 600

Method 2: Upside-Down Division Method

On dividing 600 by its smallest prime factor which is 2 we get,

600/2 = 30

300 is now divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1.
The prime factorization of 600:

Prime Factorization of 600

Hence, the prime factors of 600 are 2, 3, and 5.
The prime factorization of 600 is 2 × 2 × 2 × 3 × 5 × 5.

Factors of 600 in Pairs

Numbers which on multiplication to each other give 600 are known as the factor pairs of 600. Let's observe the following table having factors of 600 in pairs. If we consider negative integers, then both the numbers in the pair factors will be negative as ( - ve × - ve ) = +ve.

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

Important Notes:

The sum of the digits of 600 is 6. As 6 is divisible by 3, 3 is one of the factors of 600.
600 is not a perfect square number. Thus, it has even number of factors.

Example 1: Shawn has a box of length 20 inches and breadth 25 inches. Is its area equal to 600 square inches?

Solution:

The area of the box of length 20 inches and 25 inches is given by the formula: area = length × breadth = 20 × 25 = 500 square inches.
Hence, the area of the box is not equal to 600 square inches.
Example 2: If the product of two factors is 600 and one of the factors is -75. Can you find which is the other factor?

Solution:

We know, 600 = Factor 1 × Factor 2
Hence, 600 =(-75) × Factor 2

Factor 2 = 600/(-75) =(-8)
Hence, the other factor is -8.

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FAQs on Factors of 600

What are the factors of 600?

The 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.

What are the prime factors of 600?

The prime factors of 600 are 2, 3, and 5.

Which factors of 600 are perfect squares?

The factors of 600 which are perfect squares are 1, 4, 25, and 100.

What are the common factors of 600 and 450?

The 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.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Hence, the common factors of 600 and 450 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

What are the negative pair factors of 600?

The negative 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), and (-24, -25).

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