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Find the biggest number which can divide both 324 and 144.
Question

Find the biggest number which can divide both 324 and 144.

A.

18

B.

36

C.

9

D.

21

Correct option is B

Given:
The numbers 324 and 144.
Formula Used:
Prime factorization of each number and the common factors.
Solution:
Prime factorization of 324:
324=22×34324 = 2^2 \times 3^4
Prime factorization of 144:
144=24×32144 = 2^4 \times 3^2​ ​​
The common factors are the minimum powers of the common prime factors:
For 2, the minimum power is 22.2^2.
For 3, the minimum power is 323^2​.
GCD =  22×32=4×9=362^2 \times 3^2 = 4 \times 9 = 36
Thus, the correct answer is (b).​​

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