1800, 2709, 3618, 4554
1800 2709 3618
1800 2709 3618 4554
The first two common multiples of 4 and 9 are 36 and 72.
The common multiples of 4 and 9 are 36, 72, 108 and so on.
There are 16 4-digit numbers that can be made up from 9 and 6.
There are 5 multiples of 9. There are 4 multiples of 12. There is 1 number that is a multiple of both, 36.
The unit digit of 3127173 is the unit digit of 7173. The other digits of 3127 are multiples of 10 and so they cannot contribute to the unit digit. Now the unit digits of the powers of 7 are Power -- Unit digit 0 -- 1 1 -- 7 2 -- 9 3 -- 3 4 -- 1 and you are back into the loop (of 1-7-9-3). So, you only need consider 7 to the power 173 modulo 4. That is, the remainder when 173 is divided by 4. 173 = 1 mod 4 So the unit digit of 3127173 is the same as the unit digit of 7173 which is the unit digit of 71 which is 7.
999
-4
There are 720 of them. The three digit counting numbers are 100-999. All multiples of 5 have their last digit as 0 or 5. There are 9 possible numbers {1-9} for the first digit, There are 10 possible numbers {0-9} for each of the first digits, There are 8 possible numbers {1-4, 6-9} for each of the first two digits, Making 9 x 10 x 8 = 720 possible 3 digit counting numbers not multiples of 5.
Any digit is possible.
Nine. The sum of the digits must be a multiple of 9; because of the repeated digits, this is only possible if the first two digits add up to 9.
The two-digit multiples of nine are 18, 27, 36, 45, 54, 63, 72, 81, 90, 99.
There are 13 two-digit multiples of 7.
There are 9*10*9 = 810 such numbers.
3
The answer depends on if 4 and 9 WHAT!
Any multiple of four must be even; any number ending in three is odd. Look at the multiples of four from 1 to 9. They are in the order : 4,8,12,16,20,24,28,32,36. Now, any number when multiplied by 4, will have the one's digit as the one's digit of the above multiples In the above multiples, no multiple has 3 as the one's digit, i.e., no multiple ends in three. Take an example. 15x4 will have 0 in the one's digit because 5x4 = 20 and has 0 in the one's place.
There are 2000 4-digit numbers that are multiples of 5, so, instead of listing them all, it is equally valid to say: Any4-digit number whose final digit is either a 5 or a 0 is a multiple of 5. Get Right? :P