What least number should be subtracted from 642 so that the remainder when divided by 5, 7, and 9 ...

What least number should be subtracted from 642 so that the remainder when divided by 5, 7, and 9 will leave in each case the same remainder 4 ?

Answer/Solution

8

Steps/Work

The LCM of 5, 7, and 9 is 315. The next multiple is 2*315 = 630.
630 + {remainder} = 630 + 4 = 634, which is 8 less than 642.
Answer: C.

General Calculator / Auto Solver

What least number should be subtracted from so that the remainder when divided by , , and will leave in each case the same remainder ?

Calculated Answer

8

Step by Step Solution

In order to solve problem, you must evaluate n₀ - (n₄ + n₃ * n₁ * n₂ * 2).

n₀ =	642
n₁ =	5
n₂ =	7
n₃ =	9
n₄ =	4

n₀ - (n₄ + n₃ * n₁ * n₂ * 2)
Evaluate n₁ * n₂ = 35
n₀ - (n₄ + n₃ * 35 * 2)
Evaluate n₃ * 35 = 315
n₀ - (n₄ + 315 * 2)
Evaluate 315 * 2 = 630
n₀ - (n₄ + 630)
Evaluate n₄ + 630 = 634
n₀ - 634
Evaluate n₀ - 634 = 8
8
The answer to the problem and the result of n₀ - (n₄ + n₃ * n₁ * n₂ * 2) is 8