Greatest Common Factor of 600 and 1050

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 600, 1050 i.e. 150 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 600 and 1050 is 150.

GCF(600,1050) = 150

GCF of 600 and 1050

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 600 and 1050

GCF of 600 and 1050 is 150

Prime Factorization of 600


2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 600 are 2,3,5. Prime factorization of 600 in exponential form is:

600 = 23×31×52

Prime Factorization of 1050


2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 1050 are 2,3,5,7. Prime factorization of 1050 in exponential form is:

1050 = 21×31×52×71

∴ So by taking common prime factors GCF of 600 and 1050 is 150

Greatest Common Factor of 600 and 1050 by matching factors method

Factors of 600

List of positive integer factors of 600 that divides 600 without a remainder.

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

Factors of 1050

List of positive integer factors of 1050 that divides 1050 without a remainder.

1,2,3,5,6,7,10,14,15,21,25,30,35,42,50,70,75,105,150,175,210,350,525,1050

Greatest Common Factor

We found the factors and prime factorization of 600 and 1050. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 1050 is 150.

Also check out the Least Common Multiple of 600 and 1050

Properties of GCF 600 and 1050

(i) The GCF of 600 and 1050 is associative

GCF of 600 and 1050 = GCF of 1050 and 600

Related Greatest Common Factor of 600

Related Greatest Common Factor of 1050

Frequently Asked Questions on GCF of 600 and 1050

1. What is the GCF of 600 and 1050?

Answer: GCF of 600 and 1050 is 150.

2. What are the Factors of 600?

Answer: 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. There are 24 integers that are factors of 600. The greatest factor of 600 is 600.

3. What are the Factors of 1050?

Answer: Factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050. There are 24 integers that are factors of 1050. The greatest factor of 1050 is 1050.

4. How to Find the GCF of 600 and 1050?

Answer:

Greatest Common Factor of 600 and 1050 = 150

Step 1: Find the prime factorization of 600

600 = 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 1050

1050 = 2 x 3 x 5 x 5 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 x 5 x 5 = 150

Step 4: Therefore, the greatest common factor of 600 and 1050 is 150