What is the Greatest Common Factor of 23674 and 23688?

Greatest common factor (GCF) of 23674 and 23688 is 14.

GCF(23674,23688) = 14

We will now calculate the prime factors of 23674 and 23688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23674 and 23688.

How to find the GCF of 23674 and 23688?

We will first find the prime factorization of 23674 and 23688. After we will calculate the factors of 23674 and 23688 and find the biggest common factor number .

Step-1: Prime Factorization of 23674

Prime factors of 23674 are 2, 7, 19, 89. Prime factorization of 23674 in exponential form is:

23674 = 2¹ × 7¹ × 19¹ × 89¹

Step-2: Prime Factorization of 23688

Prime factors of 23688 are 2, 3, 7, 47. Prime factorization of 23688 in exponential form is:

23688 = 2³ × 3² × 7¹ × 47¹

Step-3: Factors of 23674

List of positive integer factors of 23674 that divides 23674 without a remainder.

1, 2, 7, 14, 19, 38, 89, 133, 178, 266, 623, 1246, 1691, 3382, 11837

Step-4: Factors of 23688

List of positive integer factors of 23688 that divides 23674 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 47, 56, 63, 72, 84, 94, 126, 141, 168, 188, 252, 282, 329, 376, 423, 504, 564, 658, 846, 987, 1128, 1316, 1692, 1974, 2632, 2961, 3384, 3948, 5922, 7896, 11844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23674 and 23688. The biggest common factor number is the GCF number.
So the greatest common factor 23674 and 23688 is 14.

Also check out the Least Common Multiple of 23674 and 23688