Question

find the largest number which divides 103 169 and241 leaving 7 as remainder in each case​

Answer 1

Given: 103, 169, 241

Step by step solution:

169-103=66

241-169=72

241-103=138

HCF of 66, 72 and 138 is 6

The largest number which can divide the three given numbers with remainder as 7 is 6.

Answer 2

Given : Largest number which divides 103 , 169 and 241 leaving 7 as remainder in each case​

To Find : the largest number

Solution:

the largest number = k

103 = ak  + 7   => ak  = 96

169  = bk + 7  => bk = 162

241 = ck + 7   => ck  = 234

HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.

HCF = product of common factors of least power

K is the HCF of ( 96 , 162 , 234 )

96 = 2 * 2 * 2 * 2 * 2 * 3

162 = 2 * 3 * 3 * 3 * 3

234 = 2 *  3 * 3 * 13

HCF  =  2 * 3    = 6

6 is the largest number

But it will leave remainder 7 - 6 = 1

as 6 < 7

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