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On dividing a number by 5, 7 and 8 successively the remainders are 2, 3 and 4 respectively. What will be the remainders if the order of division is reversed?

On dividing a number by 5, 7 and 8 successively the remainders are 2, 3 and 4 respectively. What will be the remainders if the order of division is reversed? Correct Answer 5, 5, 2

Concept used:

Successive Division = If we divide a number by a particular number, then again the resulting quotient by a number, and again ......., this is called successive division

Calculation:

We will try to get the real number by going by the last number first

So, Now talking 8 as divisor, 1 as quotient and 4 as remainder

⇒ 8 × 1 + 4 = 12

Now, taking 7 as divisior, 12 as quotient and 3 as remainder

⇒ 7 × 12 + 3 = 87

Now, taking 5 as divisior, 87 as quotient and 2 as remainder

⇒ 5 × 87 + 2 = 437

So, the number may be 437

When order of division is reversed

Dividing 437 by 8

⇒ 8 × 54 + 5

Now, dividing quotient 54 by 7

⇒ 7 × 7 + 5

Now, dividing quotient 7 by 5

⇒ 5 × 1 + 2

∴ We get remainders 5, 5, 2

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