What is the Greatest Common Factor of 67410 and 67424?

Greatest common factor (GCF) of 67410 and 67424 is 14.

GCF(67410,67424) = 14

We will now calculate the prime factors of 67410 and 67424, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67410 and 67424.

How to find the GCF of 67410 and 67424?

We will first find the prime factorization of 67410 and 67424. After we will calculate the factors of 67410 and 67424 and find the biggest common factor number .

Step-1: Prime Factorization of 67410

Prime factors of 67410 are 2, 3, 5, 7, 107. Prime factorization of 67410 in exponential form is:

67410 = 2¹ × 3² × 5¹ × 7¹ × 107¹

Step-2: Prime Factorization of 67424

Prime factors of 67424 are 2, 7, 43. Prime factorization of 67424 in exponential form is:

67424 = 2⁵ × 7² × 43¹

Step-3: Factors of 67410

List of positive integer factors of 67410 that divides 67410 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 107, 126, 210, 214, 315, 321, 535, 630, 642, 749, 963, 1070, 1498, 1605, 1926, 2247, 3210, 3745, 4494, 4815, 6741, 7490, 9630, 11235, 13482, 22470, 33705

Step-4: Factors of 67424

List of positive integer factors of 67424 that divides 67410 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 43, 49, 56, 86, 98, 112, 172, 196, 224, 301, 344, 392, 602, 688, 784, 1204, 1376, 1568, 2107, 2408, 4214, 4816, 8428, 9632, 16856, 33712

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67410 and 67424. The biggest common factor number is the GCF number.
So the greatest common factor 67410 and 67424 is 14.

Also check out the Least Common Multiple of 67410 and 67424