BECE Mathematics 2018 Paper

H.C.F. means Highest Common FactorFinding H.C.F. using Prime FactorsStep I:Find the prime factorization of each of the given numbers. Step II:The product of all common prime factors is the HCF of the given numbers.Prime number is a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11, 13,17 etc.)Applying the above to find the H.C.F of 18,36 and 60 Step I:$18=2 \times 9=2 \times 3 \times 3=2 \times 3^2$NOTE: $a \times a=a^1 \times a^1$From the law of indices, $a^m \times a^n=a^{m+n}$Hence $3 \times 3=3^1 \times 3^1=3^{1+1}=3^2$$\;36=18 \times 2=2 \times 3 \times 3 \times 2=2 \times 2 \times 3 \times 3=2^2 \times 3^2$$\;60=2 \times 30=2 \times 2 \times 15=2 \times 2 \times 3 \times 5=2^2 \times 3 \times 5$Step II:The product of all common prime factors is $2 \times 3$