Mathematics
Find the GCD of the given numbers by prime factorisation method:
(i) 24, 45
(ii) 180, 252, 324
Answer
(i) 24, 45
Prime factorisation of the given numbers are:
24 = 2 × 2 × 2 × 3
45 = 3 × 3 × 5
The only common prime factor is 3 (appearing once in each).
Hence, GCD of 24 and 45 = 3.
(ii) 180, 252, 324
Prime factorisation of the given numbers are:
180 = 2 × 2 × 3 × 3 × 5
252 = 2 × 2 × 3 × 3 × 7
324 = 2 × 2 × 3 × 3 × 3 × 3
The common prime factors are 2 (twice) and 3 (twice) in all three numbers.
Hence, GCD of 180, 252 and 324 = 2 × 2 × 3 × 3 = 36.
Related Questions
In 92*389, replace * by a digit so that the number formed is divisible by 11.
Find the prime factorisation of the following numbers:
(i) 168
(ii) 2304
Find the HCF of the given numbers by division method:
(i) 54, 82
(ii) 84, 120, 156
Find the LCM of the given numbers by prime factorisation method:
(i) 27, 90
(ii) 36, 48, 210