Find the greatest number that will divide that will divide 43, 91 and 183 so as to leave the same remainder in each case.

Foundation

Mathematics Foundation

HCF and LCM

Properties of Real Number

Linear Equations in One Variable

Question

Find the greatest number that will divide that will divide 43, 91 and 183 so as to leave the same remainder in each case.

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Given numbers are

43, 91

and

183.

Subtract smallest number from both the highest numbers.

we have three cases :

183 &gt; 43

;

183 &gt;91

and

91 &gt; 43

183 - 43 = 140

183 - 91 = 92

and

91 - 43 = 48

Now , we have three new numbers :

140, 48

and

92

For HCF of

140, 48

and

92

using prime factorization method, we get
HCF

(140, 48

and

92) = 4

the highest number that divide

183, 91

and

43

and leave the same remainder is

4.