What is the Greatest Common Factor of 74000 and 74010?

Greatest common factor (GCF) of 74000 and 74010 is 10.

GCF(74000,74010) = 10

We will now calculate the prime factors of 74000 and 74010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74000 and 74010.

How to find the GCF of 74000 and 74010?

We will first find the prime factorization of 74000 and 74010. After we will calculate the factors of 74000 and 74010 and find the biggest common factor number .

Step-1: Prime Factorization of 74000

Prime factors of 74000 are 2, 5, 37. Prime factorization of 74000 in exponential form is:

74000 = 2⁴ × 5³ × 37¹

Step-2: Prime Factorization of 74010

Prime factors of 74010 are 2, 3, 5, 2467. Prime factorization of 74010 in exponential form is:

74010 = 2¹ × 3¹ × 5¹ × 2467¹

Step-3: Factors of 74000

List of positive integer factors of 74000 that divides 74000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 50, 74, 80, 100, 125, 148, 185, 200, 250, 296, 370, 400, 500, 592, 740, 925, 1000, 1480, 1850, 2000, 2960, 3700, 4625, 7400, 9250, 14800, 18500, 37000

Step-4: Factors of 74010

List of positive integer factors of 74010 that divides 74000 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 2467, 4934, 7401, 12335, 14802, 24670, 37005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74000 and 74010. The biggest common factor number is the GCF number.
So the greatest common factor 74000 and 74010 is 10.

Also check out the Least Common Multiple of 74000 and 74010