Question

When a natural number divided by a certain divisor,
we get 15 as a remainder. But when the 10 times
of the same number is divided by the same divisor
we get 6 as a remainder. The maximum possible
number of such divisors is :
​

Answer 1

Step-by-step explanation:

$Let N be the number and d be the divisor then N=dQ +15</p><p>Again, 10N=10(dQ+15)</p><p>⟹10 N=10dQ+150</p><p>⟹10N+d10Q+144+6</p><p>⟹10N=(d×10Q+144)+6</p><p>⟹10N=d(10Q+144/d)+6</p><p>∴144 must be divisible by d, Thus the probable value of d are 1,2,3,4,6,8,9,12,16,18,24,36,48,72,144</p><p>(as these numbers are the factors of 144)</p><p>But be value of divisor d must be greater</p><p> than the remainder (here 6 and 15 )so. 1,2,3,4,6,8,9,12 can not be the value. of d. Hence only 7 value (greater than 15) are possible.$

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