BECE Mathematics 2018 Paper

Concept:H.C.F. means Highest Common Factor. It is the largest number that divides all the given numbers exactly. To find it, take the product of the common prime factors with their lowest powers.Explanation:First, write the prime factorization of each number.$18 = 2 \times 3 \times 3 = 2 \times 3^2$$36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2$$60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5$Now, identify the prime factors common to all three numbers: $2$ and $3$.For each common prime factor, choose the smallest power that appears in the factorizations.Smallest power of $2$ is $2^1$.Smallest power of $3$ is $3^1$.Therefore, H.C.F. $= 2^1 \times 3^1 = 2 \times 3 = 6$.This matches option D.Answer:The H.C.F. of $18$, $36$ and $60$ is $2 \times 3 = 6$.Correct option: D.