Divisibility Rules

Learning Objectives Identify numbers divisible by 2, 3, 4, 5, 6, 9, and 10. Apply divisibility rules to determine if a given number is divisible by another without performing long division. Explain the reasoning behind common divisibility rules, such as those for 3 and 9. Solve problems involving divisibility criteria for various numbers. Differentiate between numbers that are divisible and those that are not, based on their properties. Recognize the efficiency and practical utility of divisibility rules in mathematical contexts. Ever wondered how to quickly tell if a large number can be divided evenly by another without doing long division? 🤔 Let's unlock the secrets to making quick mental math checks! In this lesson, you'll learn powerful shortcuts called divis...

TermDefinitionExample DivisibleA number is divisible by another number if, when divided, the result is a whole number with no remainder.12 is divisible by 3 because 12 ÷ 3 = 4 (a whole number with no remainder). FactorA factor of a number is an integer that divides the number evenly, leaving no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. MultipleA multiple of a number is the product of that number and any integer. It's a number that can be divided by another number without a remainder.Multiples of 3 include 3, 6, 9, 12, etc. RemainderThe amount left over after division when one number cannot be divided exactly by another.When 13 is divided by 3, the quotient is 4 with a remainder of 1. Digit SumThe sum of the individual digits of a number. This concept is crucial for divis...

Divisibility Rule for 2 A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). This rule is used to quickly check if a number can be divided into two equal groups. Look only at the very last digit of the number. Divisibility Rule for 3 A number is divisible by 3 if the sum of its digits is divisible by 3. Mathematically, if a number $N = d_k d_{k-1} ... d_1 d_0$, then $N$ is divisible by 3 if $d_k + d_{k-1} + ... + d_1 + d_0$ is divisible by 3. To use this rule, add all the individual digits of the number. If that sum is a multiple of 3, then the original number is divisible by 3. Divisibility Rule for 5 A number is divisible by 5 if its last digit is 0 or 5. This rule is very straightforward. Just check the digit in the ones place. If it&...