SOLUTION: find the least natural number that has the remainder 3 when divided by 5. the remainder 5 when divided by 7 and the remainder 8 when divided by 10

Question 1120812: find the least natural number that has the remainder 3 when divided by 5. the remainder 5 when divided by 7 and the remainder 8 when divided by 10
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

(1) Notice that when the number, n, is divided by each of 5, 7, and 10, the remainder in each case is 2 less than the divisor. That means the number n+2 is divisible by 5, 7, and 10.

The least natural number divisible by 5, 7 and 10 is 70; the number we are looking for is 70-2 = 68.

or...
(2) The number leaves a remainder of 8 when divided by 10; the units digit of the number must be 8.

If the number has units digit 8, and dividing it by 7 leaves a remainder of 5, then 5 less than the number must be a multiple of 7 with units digit 3. The smallest such natural number is 63; the number we are looking for is 63+5 = 68.

And there are numerous other ways you could solve the problem....
RELATED QUESTIONS
What is the least number that when divided by 7 has a remainder of 4, and when divided by (answered by robertb)

What is that number , when that number is divided by 9 the remainder is 8 , when that... (answered by AnlytcPhil)

A certain number leaves a remainder of 4 when divided by 5, a remainder of 5 when divided (answered by ikleyn,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)

What is the smallest whole number that has a remainder of 1 when divided by 4, a... (answered by RAY100)

Find the smallest number that gives a remainder of 1 when divided by 4, a remainder of 2... (answered by richwmiller)

Find the least number which when divided by 6, 8, and 15 leaves a remainder 5, but when... (answered by Edwin McCravy)

a number when divided by 5, gives a remainder 3. Find the remainder when square of that... (answered by josmiceli)

What is the smallest positive number that when divided by 7, the remainder is 6 and when... (answered by ikleyn)