When dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been:
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When the number was divided by 585, it would yield a remainder of 584
Step-by-step explanation:
If z was the last number to be successively divided by 13, it yielded the remainder of 12. Thus, a remainder of 12 indicates that the value of 1 less than being divisible by 13.
Hence, it is calculated as:
Z = 13 x 1 + 12 = 25
The last number is 25.
Let the previous number is denoted as y
Value of y = 9 x z + 8
= 9 x 25 + 8
= 233
The value of the earlier number is 233
Let the original number be x
The value of x is calculated as = 5 × y + 4
= 5 × 233 + 4
= 1169
Thus, the original number is 1169
When 1169 was divided by 585, it would yield a remainder of 584
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