Grade 5 (age 10-11)

Divisors & Multiples

A divisor divides another number evenly, and a multiple is that number taken a whole number of times. The divisors of 12 are 1, 2, 3, 4, 6, and 12, while the multiples of 3 run on as 3, 6, 9, and beyond. The greatest common divisor and least common multiple help you share things equally or match repeating cycles. Here you slide the two numbers and find them on a Venn diagram and a number line.

What is a divisor?

🍰 A divisor is a number that divides evenly

①If a cake can be split equally to 12 people, 12 is a multiple of that number

②Conversely, numbers that divide 12 (1,2,3,4,6,12) are its divisors

③A divisor always includes 1 and itself!

Common Divisors & GCD

First number12

Second number18

🔍 Common Divisors & GCD

①Divisors shared by both numbers are common divisors

②The largest common divisor is the GCD

③The numbers in the overlap are the common divisors!

Common Multiples & LCM

🎯 Common Multiples & LCM

①Multiples shared by both numbers are common multiples

②The smallest common multiple is the LCM

③The first overlap on the number line is the LCM!

Summary

Divisor & Multiple Relation

A divides B ⇔ B is a multiple of A

If A × n = B, then A is a divisor of B and B is a multiple of A

GCD × LCM Relation

A × B = GCD(A,B) × LCM(A,B)

Product of two numbers = GCD × LCM

🎯 Key Points

①Divisor: divides evenly

②Multiple: product of the number

③GCD: largest common divisor

④LCM: smallest common multiple

⑤Product of two numbers = GCD × LCM

Examples and Unit Test

Example 1

Find all the divisors of 12.

Find numbers that divide 12 evenly, from 1: 1, 2, 3, 4, 6, 12.

12 ÷ 1=12, ÷2=6, ÷3=4, ÷4=3, ÷6=2, ÷12=1; all divide evenly.

▸ 1, 2, 3, 4, 6, 12

A divisor always includes 1 and the number itself.

Example 2

Find the GCD of 12 and 18.

Divisors of 12: 1,2,3,4,6,12 / Divisors of 18: 1,2,3,6,9,18.

The common divisors are 1, 2, 3, 6; the largest is the GCD.

▸ 6

The greatest of the common divisors is the GCD.

Unit Test

What is the LCM of 4 and 6?

①2

②12

③24

④10

▸ ② 12

Multiples of 4: 4,8,12,16,... / Multiples of 6: 6,12,18,...

The smallest common multiple is 12, so the LCM is 12.

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Quadrilateral Types

Prime & Composite