Question: A factory produces two types of boxes, one with 56 chocolates and another with 42 chocolates. If the factory wants to package the chocolates into boxes of equal size without any chocolates left over, what is the largest size for each box?
A) 6 chocolates
B) 14 chocolates
C) 21 chocolates
D) 28 chocolates
Solution:
To find the largest box size, we calculate the HCF of 56 and 42.
Prime factorization of 56:56 = 2³ × 7
Prime factorization of 42:42 = 2 × 2 × 7
The common factors are 2¹ and 7¹.
Thus, the HCF is:
2¹ × 7¹ = 14 chocolates
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