Q9 of 56 Page 17

If H.C.F of 144 and 180 are expressed in the form 13m –3, find the value of m.

Prime factorizing 144 and 180 we get,


144 = 24 × 32


180 = 22 × 5 × 32


∴ H.C.F (180, 144) = 22 × 3 2


= 4 × 9


= 36


But given H.C.F can be expressed in the form 13m – 3


∴ 13 m – 3 = 36


⇒ 13 m = 39


⇒ m = 3


⇒ m = 3


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