Question: A teacher has 96 crayons and 144 markers. She wants to divide them into the largest possible groups such that each group has the same number of crayons and the same number of markers. How many crayons will be in each group?
(A) 12 crayons
(B) 24 crayons
(C) 36 crayons
(D) 48 crayons
Solution:
We need to find the HCF of 96 and 144.
Prime factorization of 96:
96 = 2⁵ × 3
Prime factorization of 144:
144 = 2⁴ × 3²
HCF is the product of the lowest powers of all common prime factors:
HCF (96,144) = 2⁴ × 3 = 16 × 3 = 48
So, each group will contain 48 crayons.
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