Mathematics
Grade 5
15 min
Divisibility rules: word problems
Divisibility rules: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify key information and the question being asked in divisibility word problems.
Select the appropriate divisibility rule (for 2, 3, 5, or 10) to solve a given word problem.
Apply divisibility rules accurately to determine if a number is divisible by another.
Explain their reasoning for using a specific divisibility rule to solve a problem.
Interpret the results of divisibility tests in the context of real-world word problems.
Formulate a clear answer to a divisibility word problem based on their findings.
Ever wonder how stores quickly arrange items into equal groups without counting every single one? 🤔 Divisibility rules are like secret shortcuts that help us solve these kinds of puzzles!
In this lesson, you'll learn how to use divisibility r...
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Key Concepts & Vocabulary
TermDefinitionExample
DivisibilityWhen one number can be divided by another number with no remainder. It means the first number is a multiple of the second number.20 is divisible by 5 because 20 ÷ 5 = 4 with no remainder.
Divisor (or Factor)The number by which another number is divided. If there's no remainder, it's also called a factor.In 18 ÷ 3 = 6, the number 3 is the divisor (and a factor of 18).
DividendThe number that is being divided in a division problem.In 18 ÷ 3 = 6, the number 18 is the dividend.
RemainderThe amount left over after dividing one number by another, when the division is not exact.When 17 is divided by 5, the remainder is 2 (because 17 = 5 × 3 + 2).
Divisibility RuleA quick way or a shortcut to determine if a number can be divided by another number withou...
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Core Formulas
Divisibility Rule for 2
A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8).
Use this rule when you need to know if a number can be split into two equal groups or if it's an even number.
Divisibility Rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Use this rule when you need to check if a number can be divided into three equal groups. Add up all the digits in the number, then check if that sum is divisible by 3.
Divisibility Rule for 5
A number is divisible by 5 if its last digit is 0 or 5.
Use this rule when you need to know if a number can be grouped into fives, like counting by fives or sharing items among five people.
Divisibility Rule for 10
A number is divisible by 10 if its last digit i...
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Challenging
A company made 1,24_ bracelets. The number of bracelets must be divisible by both 2 and 3. What digit must go in the blank to make this true?
A.0
B.5
C.2
D.3
Challenging
I am a 3-digit number of stickers in a prize box. My last digit is 0. The sum of my digits is 9. Which of these group sizes can I be divided into with no remainder?
A.Only groups of 10
B.Groups of 2, 3, 5, and 10
C.Only groups of 3 and 5
D.Only groups of 2 and 10
Challenging
A school has 435 students. The principal finds that teams of 3 are possible and teams of 5 are possible. However, teams of 10 are not possible. Why can the students be grouped into teams of 5 but not teams of 10?
A.Because 435 is an odd number.
B.Because the number ends in 5, which works for the rule of 5, but not in 0, which is required for the rule of 10.
C.Because the sum of the digits (4+3+5=12) is not divisible by 10.
D.Because 10 is a bigger number than 5.
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