The 9 times table
1*9 = 9
2*9 = 18
3*9 = 27
4*9 = 36
5*9 = 45
6*9 = 54
7*9 = 63
8*9 = 72
9*9 = 81
10*9 = 90
11*9 = 99
12*9 = 108
All the ones in bold are two digit numbers divisible by 9 because they are multiples of 9. THAT IS WHY YOU SHOULD LEARN YOUR TIMES TABLES!
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987
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.
All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.
There are five numbers: 18, 36, 54, 72, 90.
1975487646
Here are two digit numbers that are divisible by both 6 and 9: 18 (which is the least common multiple) 36 54 72 90
987
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.
All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.
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.
There are five numbers: 18, 36, 54, 72, 90.
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.
1975487646
There are 278 5-digit numbers less than 20,000 that are divisible by both four and nine.
There are 5! = 120 such numbers.
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).
3, 6, 9