What is the Greatest Common Factor of 63000 and 63014?

Greatest common factor (GCF) of 63000 and 63014 is 14.

GCF(63000,63014) = 14

We will now calculate the prime factors of 63000 and 63014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 63000 and 63014.

How to find the GCF of 63000 and 63014?

We will first find the prime factorization of 63000 and 63014. After we will calculate the factors of 63000 and 63014 and find the biggest common factor number .

Step-1: Prime Factorization of 63000

Prime factors of 63000 are 2, 3, 5, 7. Prime factorization of 63000 in exponential form is:

63000 = 2³ × 3² × 5³ × 7¹

Step-2: Prime Factorization of 63014

Prime factors of 63014 are 2, 7, 643. Prime factorization of 63014 in exponential form is:

63014 = 2¹ × 7² × 643¹

Step-3: Factors of 63000

List of positive integer factors of 63000 that divides 63000 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 50, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 120, 125, 126, 140, 150, 168, 175, 180, 200, 210, 225, 250, 252, 280, 300, 315, 350, 360, 375, 420, 450, 500, 504, 525, 600, 630, 700, 750, 840, 875, 900, 1000, 1050, 1125, 1260, 1400, 1500, 1575, 1750, 1800, 2100, 2250, 2520, 2625, 3000, 3150, 3500, 4200, 4500, 5250, 6300, 7000, 7875, 9000, 10500, 12600, 15750, 21000, 31500

Step-4: Factors of 63014

List of positive integer factors of 63014 that divides 63000 without a remainder.

1, 2, 7, 14, 49, 98, 643, 1286, 4501, 9002, 31507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 63000 and 63014. The biggest common factor number is the GCF number.
So the greatest common factor 63000 and 63014 is 14.

Also check out the Least Common Multiple of 63000 and 63014