What is the Greatest Common Factor of 2050 and 2070?

Greatest common factor (GCF) of 2050 and 2070 is 10.

GCF(2050,2070) = 10

We will now calculate the prime factors of 2050 and 2070, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2050 and 2070.

How to find the GCF of 2050 and 2070?

We will first find the prime factorization of 2050 and 2070. After we will calculate the factors of 2050 and 2070 and find the biggest common factor number .

Step-1: Prime Factorization of 2050

Prime factors of 2050 are 2, 5, 41. Prime factorization of 2050 in exponential form is:

2050 = 2¹ × 5² × 41¹

Step-2: Prime Factorization of 2070

Prime factors of 2070 are 2, 3, 5, 23. Prime factorization of 2070 in exponential form is:

2070 = 2¹ × 3² × 5¹ × 23¹

Step-3: Factors of 2050

List of positive integer factors of 2050 that divides 2050 without a remainder.

1, 2, 5, 10, 25, 41, 50, 82, 205, 410, 1025

Step-4: Factors of 2070

List of positive integer factors of 2070 that divides 2050 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 690, 1035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2050 and 2070. The biggest common factor number is the GCF number.
So the greatest common factor 2050 and 2070 is 10.

Also check out the Least Common Multiple of 2050 and 2070