Question

# What is the remainder when 1281000 is divided by 153?

A
103
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B
145
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C
118
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D
52
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Solution

## The correct option is D 52We can solve this by splitting the denominator into two co-prime numbers 9 and 17. First find the remainder of 1281000 on division by 9. 1281000÷9→21000÷9=(26)166×24÷9→Remainder=7. This means that 1281000 is a 9n + 7 number. Next find the remainder of 1281000 on division by 17. 1281000÷17→91000÷17=[(916)62×98]÷17→Remainder=1. This means that 1281000 is a 17n + 1 number. If we try to look for a number below 153, that is both 17n + 1 as well as 9n + 7, we would see that the number 52 fulfills this requirement. Hence, 52 is the required remainder of 1281000÷153

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