What is the Greatest Common Factor of 33824 and 33840?

Greatest common factor (GCF) of 33824 and 33840 is 16.

GCF(33824,33840) = 16

We will now calculate the prime factors of 33824 and 33840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33824 and 33840.

How to find the GCF of 33824 and 33840?

We will first find the prime factorization of 33824 and 33840. After we will calculate the factors of 33824 and 33840 and find the biggest common factor number .

Step-1: Prime Factorization of 33824

Prime factors of 33824 are 2, 7, 151. Prime factorization of 33824 in exponential form is:

33824 = 2⁵ × 7¹ × 151¹

Step-2: Prime Factorization of 33840

Prime factors of 33840 are 2, 3, 5, 47. Prime factorization of 33840 in exponential form is:

33840 = 2⁴ × 3² × 5¹ × 47¹

Step-3: Factors of 33824

List of positive integer factors of 33824 that divides 33824 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 151, 224, 302, 604, 1057, 1208, 2114, 2416, 4228, 4832, 8456, 16912

Step-4: Factors of 33840

List of positive integer factors of 33840 that divides 33824 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 47, 48, 60, 72, 80, 90, 94, 120, 141, 144, 180, 188, 235, 240, 282, 360, 376, 423, 470, 564, 705, 720, 752, 846, 940, 1128, 1410, 1692, 1880, 2115, 2256, 2820, 3384, 3760, 4230, 5640, 6768, 8460, 11280, 16920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33824 and 33840. The biggest common factor number is the GCF number.
So the greatest common factor 33824 and 33840 is 16.

Also check out the Least Common Multiple of 33824 and 33840