Divisibility Rules

1. Divisible – When one number divides another number with no remainder Divisibility Rules 2 – If the number ends in 2, 4, 6, 8, or 0 3 – If the digits add up to 3, 6, or 9 5 – If the number ends in 0 or 5 6 – If the rules for 2 and 3 work 9 – If the digits add up to 9 10 – If the number ends in 0

2. Divisibility Rules 2 – If the number ends in 2, 4, 6, 8, or 0 3 – If the digits add up to 3, 6, or 9 5 – If the number ends in 0 or 5 6 – If the rules for 2 and 3 work 9 – If the digits add up to 9 10 – If the number ends in 0 1) 111 2) 405 3) 635 4) 863 5) 582 6) 2124 7) 700 8) 4200 • 3 3, 5, and 9 • only 5 NONE • 2, 3, and 6 2, 3, 6, and 9 • 2, 5, and 10 2, 3, 5, 6, and 10

3. The ones digit is 5 and 5 is not divisible by 2. no yes The sum of the digits is or 12 and 12 is divisible by 3. The ones digit is 5. yes 435 is not divisible by 2, so it cannot be divisible by 6. no The ones digit is not 0. no Example 1-1a Determine whether 435 is divisible by 2, 3, 5, 6, or 10. Answer: So, 435 is divisible by 3 and 5.

4. Example 1-1b Determine whether 786 is divisible by 2,3,5,6, or 10. Answer: 786 is divisible by 2, 3, and 6.

5. The ones digit of 306 is not 0 or 5. no 306 is divisible by 2 and 3, so it is also divisible by 6. Therefore, there would beno pens left over. yes no The ones digit is not 0. Example 1-2a Student ElectionsSonya is running for student council president. She wants to give out campaign flyers with a pen to each student in the school. She can buy “Vote for Sonya” pens in packages of 5, 6, or 10. If there are 306 students in the school and she wants no pens left over, which size packages should she buy? Answer: Sonya should buy pens in packages of 6.

6. Example 1-2b TransportationA class of 72 students is taking a field trip. The transportation department can provide vans that seat 5, 6, or 10 students. If the teacher wants all vans to be the same size and no empty seats, what size vans should be used? Answer: Vans that seat 6 should be used.