What is the Greatest Common Factor of 1050 and 1064?

Greatest common factor (GCF) of 1050 and 1064 is 14.

GCF(1050,1064) = 14

We will now calculate the prime factors of 1050 and 1064, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1050 and 1064.

How to find the GCF of 1050 and 1064?

We will first find the prime factorization of 1050 and 1064. After we will calculate the factors of 1050 and 1064 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 1064

Prime factors of 1064 are 2, 7, 19. Prime factorization of 1064 in exponential form is:

1064 = 2³ × 7¹ × 19¹

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 1064

List of positive integer factors of 1064 that divides 1050 without a remainder.

1, 2, 4, 7, 8, 14, 19, 28, 38, 56, 76, 133, 152, 266, 532

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1050 and 1064. The biggest common factor number is the GCF number.
So the greatest common factor 1050 and 1064 is 14.

Also check out the Least Common Multiple of 1050 and 1064