How do you use divisibility rules to determine is a number is prime or composite?

A number is divisible by another number if the quotient is a whole number with no remainder. 42 ÷ 6 = 7 Quotient

Divisibility Rules A number is divisible by. . . Divisible Not Divisible 2 if the last digit is even (0, 2, 4, 6, or 8). 3,978 4,975 3 if the sum of the digits is divisible by 3. 315 139 4 if the last two digits form a number divisible by 4. 8,512 7,518 5 if the last digit is 0 or 5. 14,975 10,978 6 if the number is divisible by both 2 and 3 48 20 9 if the sum of the digits is divisible by 9. 711 93 10 if the last digit is 0. 15,990 10,536

Example 1: Checking Divisibility Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5 The last digit, 2, is even. Divisible The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3. Divisible The last two digits form the number 62. 62 is not divisible by 4. Not divisible Not divisible The last digit is 2. So 462 is divisible by 2 and 3.

Example 1B: Checking Divisibility Tell whether 540 is divisible by 6, 9, and 10. 6 9 10 The number is divisible by both 2 and 3. Divisible The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 540 is divisible by 6, 9, and 10.

So 114 is divisible by 2 and 3. 2 3 4 5 The last digit, 4, is even. Check It Out: Example 1A Tell whether 114 is divisible by 2, 3, 4, and 5. 2 3 4 5 The last digit, 4, is even. Divisible The sum of the digits is 1 + 1 + 4 = 6. 6 is divisible by 3. Divisible The last two digits form the number 14. 14 is not divisible by 4. Not Divisible Not Divisible The last digit is 4. So 114 is divisible by 2 and 3.

Check It Out: Example 1B Tell whether 810 is divisible by 6, 9, and 10. 6 9 10 The number is divisible by both 2 and 3. Divisible The sum of the digits is 8 + 1 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 810 is divisible by 6, 9, and 10.

Any number greater than 1 is divisible by at least two numbers—1 and the number itself. Numbers that are divisible by more than two numbers are called composite numbers. A prime number is divisible by only the numbers 1 and itself. For example, 11 is a prime number because it is divisible by only 1 and 11. The numbers 0 and 1 are neither prime nor composite.

Click to see which numbers from 1 through 50 are prime. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Tell whether each number is prime or composite. divisible by 1, 31 prime D. 18 divisible by 1, 2, 3, 6, 9, 18 composite

Tell whether each number is prime or composite. divisible by 1, 3, 9, 27 composite B. 24 divisible by 1, 2, 3, 4, 6, 8, 12, 24 composite

Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, and 10. 1. 256 2. 720 3. 615 Tell whether each number is prime or composite. 4. 47 5. 38 divisible by 2, 4 divisible by 2, 3, 4, 5, 6, 9, 10 divisible by 3, 5 prime composite