SOLUTION: What is the greatest number of 5 digits which when divided by 16, 24, 30 and 36, 10 will remainder in each case?
Algebra.Com
Question 982672: What is the greatest number of 5 digits which when divided by 16, 24, 30 and 36, 10 will remainder in each case?
Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
Let x be the unknown number.
Then x-10 is divisible by 16, 24, 30 and 36, according to the condition.
It implies that x-10 is divisible by , and .
Hence, x-10 is divisible by 16*5*9 = 720.
The greatest 5-digits number divided by 720 is 99360 (it is easy to check).
It means that x-10 = 99360.
Hence, x = 99370.
RELATED QUESTIONS
find the greatest number which leaves a remainder 10 in each case when divided by 56, 84 (answered by ikleyn)
find the smallest number which when divided by 24 and 36 leaves remainder 8 in each... (answered by KMST)
When 655, 528 and 698 are in turn divided by a certain number, the remainder is 5 in each (answered by Alan3354)
find the greatest four digit number which on being divided by 6,12,18,24,and 30 leaves... (answered by Edwin McCravy)
Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of (answered by ikleyn)
What is the smallest positive integer which, when divided by each of 2, 3, 4, 5, 6
and... (answered by greenestamps)
find the lowest natural number which when divided by 112, 140, and 168 leaves a remainder (answered by ankor@dixie-net.com)
The natural number n is the smallest number satisfying the following properties: when... (answered by ankor@dixie-net.com,fcabanski,richard1234)
find greatest number of four digits which when divided by 3,5,7,9 leaves remainder... (answered by Edwin McCravy)