Question

find the greatest number that will divide 138 183 and 243 leaving the same remainder 3 in each case

Answer 1

Given:

find the greatest number that will divide 138 183 and 243 leaving the same remainder 3 in each case

To find:

The greatest number

Solution:

138 - 3 = 135

183 - 3 = 180

243 - 3 = 240

HCF of 130, 180 and 240:

135 = 5 x 3 x 3 x 3

180 =  5 x 3 x 3 x 2 x 2

240 = 5 x 3 x 2 x 2 x 2 x 2

Highest Common Factor = 5 x 3 = 15

Greatest number that will divide 138 183 and 243 leaving the same remainder 3 in each case is 15

Answer 2

Required number =HCF of (138-3),

(183-3), (243-3)

 =HCF of 135, 180

 and 240.

we first find the HCF of 135 and 180.



Divide 135 and 180, then the remainder 45 and 135.

therefore, HCF of 135 and 180 is 45.

Now, we find the HCF of 45 and 240.

Divide 45 and 240 then the remainder 15 and 45

Therefore, HCF of 45 and 240 is 15.

Consequently, the HCF of 135, 180 and 240 is 15.

hence, the required number is 15

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