Section 2.2 Prime Numbers and Factorization 107 Answers 2. Divisible by 2 3. Divisible by 3 and 5 4. Divisible by 2, 3, 5, and 10 Divisibility Rules for 2, 3, 5, and 10 • Divisibility by 2. A whole number is divisible by 2 if it is an even number. That is, the ones-place digit is 0, 2, 4, 6, or 8. Examples: 26 and 384 • Divisibility by 3. A whole number is divisible by 3 if the sum of its digits is divisible by 3. Example: 312 (sum of digits is which is divisible by 3) • Divisibility by 5. A whole number is divisible by 5 if its ones-place digit is 5 or 0. Examples: 45 and 260 • Divisibility by 10. A whole number is divisible by 10 if its ones-place digit is 0. Examples: 30 and 170 3 1 2 6 Applying the Divisibility Rules Example 2 Determine whether the given number is divisible by 2, 3, 5, or 10. a. 624 b. 82 c. 720 Solution: Test for Divisibility a. 624 By 2: Yes. The number 624 is even. By 3: Yes. The sum 6 2 4 12 is divisible by 3. By 5: No. The ones-place digit is not 5 or 0. By 10: No. The ones-place digit is not 0. b. 82 By 2: Yes. The number 82 is even. By 3: No. The sum 8 2 10 is not divisible by 3. By 5: No. The ones-place digit is not 5 or 0. By 10: No. The ones-place digit is not 0. c. 720 By 2: Yes. The number 720 is even. By 3: Yes. The sum 7 2 0 9 is divisible by 3. By 5: Yes. The ones-place digit is 0. By 10: Yes. The ones-place digit is 0. TIP: When in doubt about divisibility, you can check by division. When we divide 624 by 3, the remainder is zero. 2. Divisibility Rules The number 20 is said to be divisible by 5 because 5 divides evenly into 20. To determine whether one number is divisible by another, we can perform the division and note whether the remainder is zero. However, there are several rules by which we can quickly determine whether a number is divisible by 2, 3, 5, or 10. These are called divisibility rules. Divisibility rules for the numbers 2, 3, 5, and 10 are used most often for factoring a number into prime factorization.We address other divisibility rules for 4, 6, 8, and 9 in the Expanding Your Skills portion of the exercises. Skill Practice Determine whether the given number is divisible by 2, 3, 5, or 10. 2. 428 3. 75 4. 2100
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