What is the Greatest Common Factor of 1050 and 1070?

Greatest common factor (GCF) of 1050 and 1070 is 10.

GCF(1050,1070) = 10

We will now calculate the prime factors of 1050 and 1070, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1050 and 1070.

How to find the GCF of 1050 and 1070?

We will first find the prime factorization of 1050 and 1070. After we will calculate the factors of 1050 and 1070 and find the biggest common factor number .

Step-1: Prime Factorization of 1050

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

1050 = 2¹ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 1070

Prime factors of 1070 are 2, 5, 107. Prime factorization of 1070 in exponential form is:

1070 = 2¹ × 5¹ × 107¹

Step-3: 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

Step-4: Factors of 1070

List of positive integer factors of 1070 that divides 1050 without a remainder.

1, 2, 5, 10, 107, 214, 535

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1050 and 1070. The biggest common factor number is the GCF number.
So the greatest common factor 1050 and 1070 is 10.

Also check out the Least Common Multiple of 1050 and 1070