What is the Greatest Common Factor of 70784 and 70800?

Greatest common factor (GCF) of 70784 and 70800 is 16.

GCF(70784,70800) = 16

We will now calculate the prime factors of 70784 and 70800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70784 and 70800.

How to find the GCF of 70784 and 70800?

We will first find the prime factorization of 70784 and 70800. After we will calculate the factors of 70784 and 70800 and find the biggest common factor number .

Step-1: Prime Factorization of 70784

Prime factors of 70784 are 2, 7, 79. Prime factorization of 70784 in exponential form is:

70784 = 2⁷ × 7¹ × 79¹

Step-2: Prime Factorization of 70800

Prime factors of 70800 are 2, 3, 5, 59. Prime factorization of 70800 in exponential form is:

70800 = 2⁴ × 3¹ × 5² × 59¹

Step-3: Factors of 70784

List of positive integer factors of 70784 that divides 70784 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 79, 112, 128, 158, 224, 316, 448, 553, 632, 896, 1106, 1264, 2212, 2528, 4424, 5056, 8848, 10112, 17696, 35392

Step-4: Factors of 70800

List of positive integer factors of 70800 that divides 70784 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 59, 60, 75, 80, 100, 118, 120, 150, 177, 200, 236, 240, 295, 300, 354, 400, 472, 590, 600, 708, 885, 944, 1180, 1200, 1416, 1475, 1770, 2360, 2832, 2950, 3540, 4425, 4720, 5900, 7080, 8850, 11800, 14160, 17700, 23600, 35400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70784 and 70800. The biggest common factor number is the GCF number.
So the greatest common factor 70784 and 70800 is 16.

Also check out the Least Common Multiple of 70784 and 70800