Question

Find HCF and LCM of 78,52 and 91 using the prime factorisation method.

Answer 1

Hint: Use the prime factorisation of numbers. Then check the Highest common factor(H.C.F.) of the numbers and Least common multiple(L.C.M.) of the numbers by looking at the prime factors obtained from the prime factorisation of the numbers.

Complete step-by-step answer:
We will find the prime factors of all the three terms individually.
Prime factors are found by a division method where we will first divide the number by 2 and if it is divisible by 2 then we will move further and will divide it by 2 till the number is divisible. This method will continue till the time we will not get 1.

2	78
3	39
13	13
	1

$78{\text{ }} = {\text{ }}2.3.13{\text{ }} = {2^1}{.3^1}{.13^1}$

2	52
2	26
13	13
	1

$52{\text{ }} = {\text{ }}2.2.13{\text{ }} = {2^2}{.13^1}$

7	91
13	13
	1

$91 = 7.13{\text{ }} = \;{7^1}{.13^1}$

HCF is the smallest power product of each factor.
Here it is $ 13 $.
LCM is the product of the highest power of each factor.
Here it is
${2^2}{.3^1}{.7^1}{.13^1}$= $1092$

Note: Break both the given numbers in the product of the powers of prime numbers. The highest common factor is the factor which is common to both the numbers and also highest. The least common multiple is the multiple of both the numbers which is least.