Find the largest number that will divide 398 , \textrm{ } 436 and 542 leaving remainders 7 , \textrm{ } 11 and 15 respectively.

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Ratio Proportion

Question

Find the largest number that will divide

398, 436

and

542

leaving remainders

7, 11

and

15

respectively.

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Clearly, the required number is the

H C F

of the numbers

398 - 7 = 391, 436 - 11 = 425,

and,

542 - 15 = 527

First we find the

H C F

391

and

425

by Euclids algorithm as given below.

Clearly,

H . C . F .

391

and

425

17

.
Let us now the

H C F

17

and the third number

527

by Euclids algorithm:

The

H C F

17

and

527

17

. Hence,

H C F

391, 4250

and

527

17

.
Hence, the required number is

17