Twelve prime numbers smaller than 100 (7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, and 83) leave the remainder 3 when divided by 4.
The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9.
There are 11 such numbers.
There are 16. Counting numbers are numbers that can be used to count whole amounts of things: 1, 2, 3, etc. (no fractions) You can divide 120 by 1 and get an answer of 120 with no remainder. Likewise you can divide 120 by 120 and get an answer of 1 with no remainder. Most of the time the answers will be in pairs. Here are all of the counting numbers that leave no remainder when divided into 120: 1, 120, 2, 60, 3, 40, 4, 30, 5, 24, 6, 20, 8, 15, 10, 12.
No, prime numbers can only be divided (and leave whole numbers) by themselves and 1 but 202 can obviously be divided by both 101 and by 2.
All even numbers greater than 2 are composite because they are all divisible by 2. Therefore, from 3 onwards, all prime numbers are odd. Consider three consecutive odd numbers. They must be of the form 2n+1, 2n+3 and 2n+5 where n is an integer. Since n is an integer, n will leave a remainder of 0, 1 or 2 when it is divided by 3. Suppose n leaves a remainder of 0 when divided by 3. Therefore n = 3k for some integer k. Then 2n+3 = 2*(3k) + 3 = 6k + 3 = 3*(2k+1). That is, middle of the three consecutive odd numbers is divisible by 3 and so it is not a prime. Now, suppose n leaves a remainder of 1 when divided by 3. Therefore n = 3k+1 for some integer k. Then 2n+1 = 2*(3k+1) + 1 = 6k+2+1 = 6k+3 = 3*(2k+1). That is, first of the three consecutive odd numbers is divisible by 3 and so it is not a prime. Finally, suppose n leaves a remainder of 2 when divided by 3. Therefore n = 3k+2 for some integer k. Then 2n+5 = 2*(3k+2) + 5 = 6k+4+5 = 6k+9 = 3*(2k+3). That is, last of the three consecutive odd numbers is divisible by 3 and so it is not a prime. Thus for any three consecutive odd numbers greater than 3, one of them is divisible by 3 and therefore the three cannot all be prime.
The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9. The infinitely many numbers that leave a remainder when divided by 9.
All numbers that leave a remainder when divided by 35.
This is an extremely poor question. There are 28 pairs of numbers and, in less than 10 minutes, I could find reasons why 17 pair were different from the other numbers in the set. A bit more time and I am sure I could do the rest. So here they are: 53 and 72: leave a remainder of 15 when divided by 19. 53 and 77: leave a remainder of 5 when divided by 12. 53 and 82: leave a remainder of 24 when divided by 29. 53 and 87: leave a remainder of 2 when divided by 17. 53 and 95: leave a remainder of 11 when divided by 21. 53 and 97: leave a remainder of 9 when divided by 11. 67 and 95: leave a remainder of 11 when divided by 28. 67 and 87: leave a remainder of 7 when divided by 17. 67 and 97: leave a remainder of 7 when divided by 30. 72 and 82: leave a remainder of 0 when divided by 2 (are even). 72 and 87: leave a remainder of 0 when divided by 3 (multiples of 3). 72 and 95: leave a remainder of 3 when divided by 23. 72 and 97: leave a remainder of 22 when divided by 25. 77 and 95: leave a remainder of 5 when divided by 9. 77 and 97: leave a remainder of 17 when divided by 20. 82 and 95: leave a remainder of 4 when divided by 13. 87 and 95: leave a remainder of 7 when divided by 8.
Eight.
They are the numbers that when divided by 2 leave a remainder of 1
0.1522
There are 11 such numbers.
0.2857
It is 98910.
Bn = 37n+1, where n is a positive integer from 1 to infinity, therefore there exists an infinite number of numbers that can be divided into 37 and leave 1 as a remainder
It is: 4710 which will leave no remainder when divided by 2 or 3
10