SOLUTION: What is the gcf of 24 and 441

Question 273720: What is the gcf of 24 and 441
Found 2 solutions by CharlesG2, solver91311:
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
What is the gcf of 24 and 441
24 = 2*2*2*3 = 8 * 3
441 = 21*21 = 3*3*7*7 = 147 * 3
GCF is 3

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Find the prime factorization of 24.

24 is even, so divisible by 2.
12 is even, so divisible by 2.
6 is even, so divisible by 2.
3 is prime.

Hence,

Find the prime factorization of 441.

441 is odd, so not divisible by 2.
441 sum of digits is 12. 12 is divisible by 3, hence 441 divisible by 3.
147 sum of digits is 12, so 147 is divisible by 3.
and 7 is prime.

Hence,

441 has no factors of 2. 24 has no factors of 7. 24 has one factor of 3 and 441 has 2 factors of 3. The fewest number of times 3 occurs is 1, hence the GCF is 3.

John

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