This Lesson (The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9) was created by by ikleyn(52781): View Source, Show About ikleyn:
The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9
Problem 1
Find the least positive integer number satisfying each of the following conditions :
- Divided by 7 gives a remainder of 4.
- Divided by 8 gives a remainder of 5.
- Divided by 9 gives a remainder of 6.
Solution
Let N be that number.
Consider the number N+3.
Then it is divisible by 7; by 8 and by 9 with no remainder.
So the number N+3 is a multiple of the product 7, 8 and 9: N+3 = 7*8*9 = 504.
Hence, N = 504-3 = 501. ANSWER
