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What is the greatest common factor (GCF) of 8 and 24 ?

Answer
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Hint: There are various methods for finding the greatest common divisor of the given numbers. The simplest method to find the greatest common divisor is by prime factorization method. In the prime factorization method, we first represent the given two numbers as a product of their prime factors and then find the product of the lowest powers of all the common factors.

Complete step by step answer:
In the given question, we are required to find the highest common factor of 8 and 24.To find the highest common factor of the given numbers: 8 and 24, first we find out the prime factors of all the numbers. We know that both the numbers given to us, 8 and 24, are composite numbers.

Composite numbers are numbers that are divisible by a number other than one and the number itself. They have more than two factors.
So, we do the prime factorization of the given numbers.
Prime factors of 8=2×2×2
Prime factors of 24=2×2×2×3
Now, the greatest common divisor is the product of the lowest powers of all the common factors. Now, we can see that there is only one repeated factor, 2 in both the numbers. Also, the number 2 is repeated thrice in the prime factors of the numbers. Hence, the least common multiple of 8 and 24 =23.
Hence, the greatest common factor (GCF) of 8 and 24 is 8.

Note: Highest common factor or the greatest common divisor is the greatest number that divides both the given numbers. Similarly, the highest common factor can also be found by using the prime factorization method as well as using Euclid’s division lemma. Highest common divisor is just a product of common factors with lowest power. Using the Euclid’s Division lemma, we try to find the combination of unique numbers q and r such that a=bq+r, where 0r<b. Here, a=24 and b=8.
So, we get,
24=8×3+0
Now, as we observe that the remainder r is zero. So, we can conclude that the number b in the last step is the greatest common factor. Hence, we get the GCF of 24 and 8 as 8.
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