What is the Greatest Common Factor of 77000 and 77014?

Greatest common factor (GCF) of 77000 and 77014 is 14.

GCF(77000,77014) = 14

We will now calculate the prime factors of 77000 and 77014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77000 and 77014.

How to find the GCF of 77000 and 77014?

We will first find the prime factorization of 77000 and 77014. After we will calculate the factors of 77000 and 77014 and find the biggest common factor number .

Step-1: Prime Factorization of 77000

Prime factors of 77000 are 2, 5, 7, 11. Prime factorization of 77000 in exponential form is:

77000 = 2³ × 5³ × 7¹ × 11¹

Step-2: Prime Factorization of 77014

Prime factors of 77014 are 2, 7, 5501. Prime factorization of 77014 in exponential form is:

77014 = 2¹ × 7¹ × 5501¹

Step-3: Factors of 77000

List of positive integer factors of 77000 that divides 77000 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 20, 22, 25, 28, 35, 40, 44, 50, 55, 56, 70, 77, 88, 100, 110, 125, 140, 154, 175, 200, 220, 250, 275, 280, 308, 350, 385, 440, 500, 550, 616, 700, 770, 875, 1000, 1100, 1375, 1400, 1540, 1750, 1925, 2200, 2750, 3080, 3500, 3850, 5500, 7000, 7700, 9625, 11000, 15400, 19250, 38500

Step-4: Factors of 77014

List of positive integer factors of 77014 that divides 77000 without a remainder.

1, 2, 7, 14, 5501, 11002, 38507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77000 and 77014. The biggest common factor number is the GCF number.
So the greatest common factor 77000 and 77014 is 14.

Also check out the Least Common Multiple of 77000 and 77014