Oh, let's paint a happy little picture with multiples of 9! If we start with 1000 and add 9 each time, we get 1008, 1017, 1026, and so on. Each of these numbers is a beautiful 4-digit multiple of 9, bringing joy and harmony to our mathematical canvas. Remember, there are countless possibilities in this magical world of numbers!
To find 4-digit multiples of 9, we need to start by determining the smallest 4-digit number divisible by 9, which is 1008 (9 x 112). The next multiple would be 1017 (9 x 113), followed by 1026 (9 x 114), and so on, increasing by increments of 9. Therefore, the 4-digit multiples of 9 range from 1008 to 9999.
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.
36 (=4*9) and its multiples.
To find the number of 4-digit numbers that are multiples of 9, we first determine the range of 4-digit numbers, which is from 1000 to 9999. Next, we calculate the first and last multiples of 9 within this range, which are 1008 and 9999 respectively. To find the total number of multiples of 9 in this range, we divide the difference between the last and first multiples by 9 and add 1, resulting in (9999 - 1008) / 9 + 1 = 999. Therefore, there are 999 4-digit numbers that are multiples of 9.
-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.
The answer depends on if 4 and 9 WHAT!
3
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