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Published byHoward Haynes Modified over 7 years ago

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

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**A number is divisible by another number if the quotient is a whole number with no remainder.**

42 ÷ 6 = 7 Quotient

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**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

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**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 = is divisible by 3. Divisible The last two digits form the number is not divisible by 4. Not divisible Not divisible The last digit is 2. So 462 is divisible by 2 and 3.

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**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 = is divisible by 9. Divisible The last digit is 0. Divisible So 540 is divisible by 6, 9, and 10.

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**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 = is divisible by 3. Divisible The last two digits form the number is not divisible by 4. Not Divisible Not Divisible The last digit is 4. So 114 is divisible by 2 and 3.

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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 = is divisible by 9. Divisible The last digit is 0. Divisible So 810 is divisible by 6, 9, and 10.

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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.

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**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

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**Tell whether each number is prime or composite.**

divisible by 1, 31 prime D. 18 divisible by 1, 2, 3, 6, 9, 18 composite

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**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

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**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. divisible by 2, 4 divisible by 2, 3, 4, 5, 6, 9, 10 divisible by 3, 5 prime composite

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