Can you list all composite numbers less than 100 whose unit's digit is 3 ?
http://www.mathsisfun.com/prime_numbers.html
To list all the composite numbers less than 100 whose units digit is 3, follow these steps:
1. Start by listing all the numbers from 10 to 99 whose unit's digit is 3. These numbers are: 13, 23, 33, 43, 53, 63, 73, 83, and 93.
2. Check if each of these numbers is composite. A composite number is any positive integer greater than 1 that has divisors other than 1 and itself. To determine if a number is composite, divide it by all the prime numbers less than it and check if any of these divisions result in a whole number.
Let's go through each number and check if it is composite:
- 13: Divide by all prime numbers less than 13 (2, 3, 5, 7, and 11). None of these divisions result in a whole number, so 13 is prime.
- 23: Divide by all prime numbers less than 23 (2, 3, 5, 7, 11, 13, 17, and 19). None of these divisions result in a whole number, so 23 is prime.
- 33: Divide by all prime numbers less than 33 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31). Dividing by 3 results in a whole number, so 33 is composite.
- 43: Divide by all prime numbers less than 43 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31). None of these divisions result in a whole number, so 43 is prime.
- 53: Divide by all prime numbers less than 53 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, and 43). None of these divisions result in a whole number, so 53 is prime.
- 63: Divide by all prime numbers less than 63 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and 61). Dividing by 3 results in a whole number, so 63 is composite.
- 73: Divide by all prime numbers less than 73 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, and 67). None of these divisions result in a whole number, so 73 is prime.
- 83: Divide by all prime numbers less than 83 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and 71). None of these divisions result in a whole number, so 83 is prime.
- 93: Divide by all prime numbers less than 93 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, and 89). Dividing by 3 results in a whole number, so 93 is composite.
So, the composite numbers less than 100 whose unit's digit is 3 are: 33 and 93.