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3, 6, 9

100. The highest 3 digit number divisible by 9 is 999 (111 times). The highest 2 digit number divisible by 9 is 99 (11 times). The difference is 100.

531 is one of them and that any 3 digit number whose digital sum is 9 is also divisible by 9

The least three-digit number that is divisible by both 5 and 9 is 135.

9 is the largest digit and so there are no digits that are divisible by 9.

All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.

Of the ten digits, 0 is the only one that is divisible by 9.

All you need to do is multiply the three numbers together:5 * 6 = 3030 * 9 = 270

144 is divisible by 12 and 9.

225

180

999

900

900

1975487646

There are 278 5-digit numbers less than 20,000 that are divisible by both four and nine.

48. Assuming no digit can be used more than once, the two digit numbers divisible by 4 are: 16, 36, 48, 56, 64, 68, 84, 96 8 of them. For any number to be divisible by 4, only the last two digits need be divisible by 4; so for three digit numbers, each of the two digit numbers above can be preceded by any of the remaining 5 digits and still be divisible by 4. → 5 x 8 = 40 three digit numbers are divisible by 4 → 40 + 8 = 48 two or three digit numbers made up of the digits {1, 3, 4, 5, 6, 8, 9} are divisible by 4. If repeats are allowed, there are an extra 2 two digit numbers (44 and 88) and each of the two digit numbers can be preceded by any of the 7 digits, making a total of 7 x 10 + 10 = 80 two and three digits numbers divisible by 4 make up of digits from the given set.

All whole numbers are divisible by 1. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Numbers are divisible by 4 if the last two digits of the number are divisible by 4. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. Numbers are divisible by 6 if they are divisible by 2 and 3. Numbers are divisible by 9 if the sum of their digits is equal to 9 or a multiple of 9. Numbers are divisible by 10 if the last digit of the number is 0.

There are 5! = 120 such numbers.

108

two NUMBERS that are divisible by three are 6 and 9.

All numbers divisible by 9 are divisible by 3, so you want all multiples of 9 that are 5 digit numbers. 10000 ÷ 9 = 11111/9 → first multiple of 9 that is a 5 digit number is 1112 x 9 = 10008 100000÷ 9 = 111111/9 → last multiple of 9 that is a 5 digit number is 11111 x 9 = 99999 → there are 11111 - 1112 + 1 = 10,000 five digit numbers that are divisible by 9 (and 3). I'll let you work some out (hint: multiple any number between 1112 and 11111 inclusive by 9).

Numbers that are co-prime won't both be divisible by nine.

Three numbers are : 3 9 and 1 * * * * * Oh dear! Those are numbers that divide into 9, not numbers that are divisible (not divisable, incidentally) by 9. Possible answers to the question are 18, 27 and 36

Last digit (0) is even, so it is divisible by 2 4 + 3 + 2 + 0 = 9 which is divisible by 3, so it is divisible by 3 last digit is 0 or 5, so it is divisible by 5 4 + 3 + 2 + 0 = 9 which is divisible by 9, so it is divisible by 9 last digit is 0, so it is divisible by 10 → 4320 is divisible by all the numbers 2, 3, 5, 9, 10