Question

write the greatest 3 digit number which is divisible by 3,4,5​

Answer 1

Step-by-step explanation:

900

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Answer 2

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3 is prime

4 has as prime factors 2*2

5 is prime

These numbers have no primes in common, so for a number to be evenly divisible by each, it must be divisible by 3*4*5=60

We know all the answers will have to be divisible by 10, which is 2*5, a couple of the primes involved. So the greatest possible answer would be 990, followed by 980 and so forth on down.

We also know that the second digit must be even, as after we divide by 10 we still need to divide by 2 again.

So now we’re looking at 980, 960, 940, and so forth on down

Finally, we know that when we add the digits together repeatedly until we have a single digit, that digit must be 3, 6, or 9, because the number is divisible by 3

980 sums to 17 which sums to 8. 960 sums to 15 which sums to 6

Since we started at the highest end of the three digit numbers and worked backwards, 960 must be the largest 3 digit number divisible by all three.

Checking our work: 960/60=16, so yes, that’s a multiple of 60. And 60 more than 960 is 1020, which isn’t a three digit number.

960 final answer

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