What is the Greatest Common Factor of 67690 and 67704?

Greatest common factor (GCF) of 67690 and 67704 is 14.

GCF(67690,67704) = 14

We will now calculate the prime factors of 67690 and 67704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67690 and 67704.

How to find the GCF of 67690 and 67704?

We will first find the prime factorization of 67690 and 67704. After we will calculate the factors of 67690 and 67704 and find the biggest common factor number .

Step-1: Prime Factorization of 67690

Prime factors of 67690 are 2, 5, 7, 967. Prime factorization of 67690 in exponential form is:

67690 = 2¹ × 5¹ × 7¹ × 967¹

Step-2: Prime Factorization of 67704

Prime factors of 67704 are 2, 3, 7, 13, 31. Prime factorization of 67704 in exponential form is:

67704 = 2³ × 3¹ × 7¹ × 13¹ × 31¹

Step-3: Factors of 67690

List of positive integer factors of 67690 that divides 67690 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 967, 1934, 4835, 6769, 9670, 13538, 33845

Step-4: Factors of 67704

List of positive integer factors of 67704 that divides 67690 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 31, 39, 42, 52, 56, 62, 78, 84, 91, 93, 104, 124, 156, 168, 182, 186, 217, 248, 273, 312, 364, 372, 403, 434, 546, 651, 728, 744, 806, 868, 1092, 1209, 1302, 1612, 1736, 2184, 2418, 2604, 2821, 3224, 4836, 5208, 5642, 8463, 9672, 11284, 16926, 22568, 33852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67690 and 67704. The biggest common factor number is the GCF number.
So the greatest common factor 67690 and 67704 is 14.

Also check out the Least Common Multiple of 67690 and 67704