Question

Rashad has 24 jolly ranchers and 56 blow pops. what is the largest number of snack bags he could make?

Answer 1

To find out the largest number of snack bags that Rashad could make, we need to find the GCF of 24 and 56

Because,

GCF of 24 and 56 is the largest possible number that divides 24 and 56 exactly without any remainder. The factors of 24 and 56 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 7, 8, 14, 28, 56 respectively.

There are 3 commonly used methods to find the GCF of 24 and 56 - long division, Euclidean algorithm, and prime factorization.

By Prime factorisation :

Prime factorization of 24 and 56 is (2 × 2 × 2 × 3) and (2 × 2 × 2 × 7) respectively.

As visible, 24 and 56 have common prime factors. Hence, the GCF of 24 and 56 is 2 × 2 × 2 = 8.

By Euclidean algorithm :

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y) where X > Y and mod is the modulo operator.

Here X = 56 and Y = 24

• GCF(56, 24) = GCF(24, 56 mod 24) = GCF(24, 8)
• GCF(24, 8) = GCF(8, 24 mod 8) = GCF(8, 0)
• GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 56 is 8.

By Long division :

GCF of 24 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 56 (larger number) by 24 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (8).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 24 and 56.

Hence,

Hence,Rashad can make 8 snack bags

Learn more about GCF at : brainly.com/question/11444998

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