A number when successively divided by 4.5 and 6 leaves
remainder 3. 2 and 4 respectively. When the order of
successive division gets reversed then find the remainders.
Answers
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Given : A number when successively divided by 4.5 and 6 leaves
remainder 3. 2 and 4 respectively.
To Find : the remainders when the order of successive division gets reversed
Solution:
Number can be defined as
4(5(6k + 4) + 2) + 3
( let say last Quotient is k hence Quotient before that 6k + 4
Hence quotient before that = 5 (6k + 4 ) + 2
and number = 4(5(6k + 4) + 2) + 3
4(5(6k + 4) + 2) + 3
= 4(30k +20 + 2) + 3
= 4(30k +22) + 3
= 120k + 88 + 3
= 120k + 91
Number is 120k + 91
order of successive division reversed hence 6 , 5 , 4
120k + 91
= 6 (20k + 15) + 1 remainder = 1
20k + 15
= 5 ( 4k + 3) remainder = 0
4k + 3 remainder = 3
remainders. are 1 , 0 , 3
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