# Going Dutch

## OBJECTIVE: To learn about divisibility rules

In this lesson, you'll learn about divisibility rules. ﻿A DIVISIBILITY RULE is a shorthand way of determining whether a given INTEGER can be evenly divided by a fixed DIVISOR without actually performing the division. The process is useful in classifying numbers as factors or multiples, prime or composite, or even or odd. A few basic definitions are in order. FACTOR                            —     one of two or more numbers that divides another number without a remainder      Examples: 1, 2, 3, 5, 6, 10, 15, and 30 are factors of 30. MULTIPLE                          —     a number that can be divided by another number without a remainder      Examples: 30 is a multiple of 1, 2, 3, 5, 6, 10, 15, and 30. EVEN NUMBER                —     a whole number that can be divided by 2 without a remainder      Examples: 0, 2, 4, 6, and 8 are the first five even numbers. Other examples are 22, 34, 46, 58, and 100. ODD NUMBER                  —     a whole number that is NOT EVEN      Examples: 1, 3, 5, 7, and 9 are the first five odd numbers. Other examples are 21, 33, 65, 87, and 99. PRIME NUMBER               —     a whole number whose only factors are 1 and itself      Examples: 2, 3, 5, 7, 11, 13, 17, and 19 are the first eight prime numbers.   COMPOSITE NUMBER     —     a whole number greater than 1 that is NOT PRIME      Examples: 21, 34, 65, 87, and 99 are composite numbers. NOTES: 2 is the SMALLEST and the ONLY EVEN prime number; the rest are ODD. 0 and 1 are neither prime nor composite.

## NOW HERE ARE THE DIVISIBILITY RULES:

Divisible by Rule Examples Nonexamples 2 — number ends in 0, 2, 4, 6, or 8 28, 96 37, 91 3 — sum of the digits is divisible by 3 51, 117 49, 115 4 — last two digits is divisible by 4 100, 216 106, 210 5 — number ends in 0 or 5 105, 255 127, 232 6 — number is divisible by BOTH 2 and 3 162, 318 158, 242 7 — difference between twice the last digit and the remaining digits is divisible by 7 245, 448 250, 459 8 — last three digits is divisible by 8 368, 696 380, 716 9 — sum of the digits is divisible by 9 765, 882 770, 895 10 — number ends in 0 980, 990 985, 999 11 — difference between the sum of the digits in odd and even positions is divisible by 11 1078, 1331 1094, 1355 12 — number is divisible by BOTH 3 and 4 1332, 1476 1350, 1485 NOTES: Any number is divisible by 1 and is equal to the NUMBER ITSELF. Division by zero is UNDEFINED.
Below is a set of problems involving divisibility rules.

## In this lesson, you learned about divisibility rules.

In future lessons, you're going to learn how to apply these rules. Did you ENJOY today's lesson?