To find the greatest common factor (GCF) of 8 and 16, we need to find the largest possible number that divides both 8 and 16 exactly without any remainder. Here are some methods to find the GCF of 8 and 16:
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Prime Factorization Method: We can find the prime factorization of 8 and 16, and then multiply the common prime factors to get the GCF. The prime factorization of 8 is 2 x 2 x 2, and the prime factorization of 16 is 2 x 2 x 2 x 2. The common prime factors are 2 x 2 x 2, so the GCF of 8 and 16 is 8.
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Euclids Algorithm: We can use Euclids algorithm to find the GCF of 8 and 16. The algorithm involves dividing the larger number by the smaller number, taking the remainder, and then dividing the smaller number by the remainder. We repeat this process until the remainder is 0. The last non-zero remainder is the GCF. Using this method, we get GCF(8, 16) = GCF(16, 8) = GCF(8, 0) = 8.
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Long Division Method: We can use long division to find the GCF of 8 and 16. We divide the larger number by the smaller number, take the remainder, and then divide the smaller number by the remainder. We repeat this process until the remainder is 0. The last non-zero remainder is the GCF. Using this method, we get GCF(8, 16) = GCF(16, 8) = GCF(8, 0) = 8.
Therefore, the GCF of 8 and 16 is 8.
