What is the Greatest Common Factor of 10074 and 10080?

Greatest common factor (GCF) of 10074 and 10080 is 6.

GCF(10074,10080) = 6

We will now calculate the prime factors of 10074 and 10080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10074 and 10080.

How to find the GCF of 10074 and 10080?

We will first find the prime factorization of 10074 and 10080. After we will calculate the factors of 10074 and 10080 and find the biggest common factor number .

Step-1: Prime Factorization of 10074

Prime factors of 10074 are 2, 3, 23, 73. Prime factorization of 10074 in exponential form is:

10074 = 2¹ × 3¹ × 23¹ × 73¹

Step-2: Prime Factorization of 10080

Prime factors of 10080 are 2, 3, 5, 7. Prime factorization of 10080 in exponential form is:

10080 = 2⁵ × 3² × 5¹ × 7¹

Step-3: Factors of 10074

List of positive integer factors of 10074 that divides 10074 without a remainder.

1, 2, 3, 6, 23, 46, 69, 73, 138, 146, 219, 438, 1679, 3358, 5037

Step-4: Factors of 10080

List of positive integer factors of 10080 that divides 10074 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10074 and 10080. The biggest common factor number is the GCF number.
So the greatest common factor 10074 and 10080 is 6.

Also check out the Least Common Multiple of 10074 and 10080