NumIO math adventure

Factor and Multiple Village

The village gates open when numbers share the right factors and multiples.

Learning goal

Find factors, multiples, common factors, common multiples, GCF, and LCM.

Skills you will practise

Factors and multiples
Common factors and common multiples
Greatest common factor and least common multiple

Worked examples

Factors of 45: 1, 3, 5, 9, 15, 45

A factor of 45 divides 45 exactly, with no remainder. Starting from 1, look for pairs of numbers whose product is 45.
1 × 45 = 45, 3 × 15 = 45 and 5 × 9 = 45. The numbers 2, 4, 6, 7 and 8 do not divide 45 exactly, so they are not factors.
The next number to try is 9, but it already appears in the pair 5 × 9, so we can stop. The factors of 45 are 1, 3, 5, 9, 15 and 45: 6 factors in all.
Factors and multiples describe the same relationship from two sides. Because 5 × 9 = 45, 5 and 9 are factors of 45, and 45 is a multiple of both 5 and 9.

GCF(42, 56) = 14

List all the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42.
List all the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56.
The numbers in both lists are the common factors: 1, 2, 7, 14. The greatest of them, 14, is the greatest common factor.
Check by dividing: 42 ÷ 14 = 3 and 56 ÷ 14 = 4. The quotients 3 and 4 share no factor other than 1, so there is no common factor greater than 14.

LCM(12, 18) = 36

Write the multiples of the larger number, 18, in order: 18, 36, 54, 72.
Look for the first one that is also a multiple of 12. 18 cannot be divided exactly by 12, but 36 ÷ 12 = 3, so 36 is a multiple of 12.
So 36 is the smallest common multiple of 12 and 18. The common multiples 36, 72, 108, … are all multiples of the least common multiple 36.
Check with the greatest common factor. The GCF of 12 and 18 is 6, and 12 = 6 × 2 and 18 = 6 × 3, so the LCM is 6 × 2 × 3 = 36.

Common mistake

Do not mix up factors and multiples. A factor divides the number exactly, so it is never larger than the number; a multiple is made by multiplying the number, so it is never smaller. Also, the least common multiple is not always the product of the two numbers: look for the first number that appears in both lists of multiples.

Teach-back question

How is a factor of a number different from a multiple of it? Why is every common multiple of two numbers a multiple of their least common multiple?

How to play

Read the short story, explore the visual model, and complete five untimed questions. Use the hint when you need a new way to think.

Classroom idea

Ask the learner to explain the model or strategy before choosing an answer, then celebrate a clear explanation as well as a correct result.

Frequently asked questions

What grade is “Factor and Multiple Village” for?

“Factor and Multiple Village” is a Grade 5 Math lesson in NumIO. It practises: factors and multiples, common factors and common multiples, greatest common factor and least common multiple.

How does the “Factor and Multiple Village” mission work?

Each mission has five untimed questions. If an answer is not right yet you can try again, and the hint button offers another way to think.

Is “Factor and Multiple Village” free, and do I need an account?

Yes, it is free and there is no account or sign-up. Progress is saved in this browser, so you can come back and continue the mission later.

Back to the adventure map

Elementary math curriculum

First discoveries

Counting Companions — Count objects carefully and match each object to one number.
Bigger, Smaller, In Order — Compare groups and numbers, then put them in a clear order.
Parts Make a Whole — Split numbers into parts and find the missing friend that makes ten.
Pattern Steps — Use equal jumps of two or five to continue a number pattern.
Number Board Trail — Move right, left, up, and down on a number board to find a number.
Add and Take Away — Join and separate small groups to solve addition and subtraction stories.

Level 1

Tens and Ones to 100 — Read two-digit numbers and see how tens and ones build each number.
Twenty-Step Addition — Add and subtract within twenty, including missing parts of an equation.
Compare and Complete — Compare numbers with words and signs, then complete a missing-number equation.
Shape and Place — Name familiar shapes and describe where objects are using position words.
Measure and Tell Time — Compare lengths, measure with a simple unit, and read an hour on a clock.
Patterns and Groups — Continue repeating patterns, sort objects by a feature, and read a small count.

Level 2

Hundreds, Tens, Ones — Build three-digit numbers with hundreds, tens, and ones.
Three-Digit Adding and Taking Away — Add and subtract three-digit numbers, including regrouping when needed.
Equal Groups and Times Tables — See multiplication as equal groups, arrays, and repeated addition.
Units and Time Journeys — Choose a useful unit, convert simple lengths, and find elapsed time.
Flat Shapes and Repeating Designs — Recognize plane figures by their properties and continue a repeating design.
Tables and Picture Graphs — Read a table or graph, compare categories, and find totals and trends.

Level 3

Multiply by grouping — Build several-digit multiplication with equal groups, arrays, and partial products.
Share and find remainders — Divide equal groups and explain both the quotient and the remainder.
Fractions and decimals — See fractions and decimals as parts of one whole and compare their sizes.
Measure the journey — Add and subtract lengths, capacities, masses, and durations with matching units.
Angles, triangles, and circles — Recognize angle sizes and describe triangles and circles with accurate measures.
Read data and relationships — Read tables and bar charts, then use a simple rule to find a related number.

Level 4

Large numbers and rounding — Read the place value of large numbers and round them to a requested place.
Big multiplication and division — Use place value, products, and equal groups to solve larger multiplication and division.
Add and subtract parts — Add and subtract fractions with the same denominator and decimals by place value.
Shape clues — Use angle clues to describe triangles and quadrilaterals and classify their properties.
Perimeter and unit paths — Find the perimeter of shapes and convert measurements between familiar units.
Lines and rules — Read change on line graphs and use a correspondence rule to predict a value.

Level 5

Factor and Multiple Village — Find factors, multiples, common factors, common multiples, GCF, and LCM.
Fraction Bridge — Simplify, make equivalent fractions, use common denominators, and add or subtract fractions.
Product Workshop — Multiply fractions and decimals and explain how the product changes.
Congruence and Symmetry Garden — Recognize congruent shapes, lines of symmetry, and rotational symmetry.
Perimeter and Area Camp — Find perimeters and areas of rectangles, squares, triangles, parallelograms, and trapezoids.
Mean and Chance Harbor — Find means and describe the chance of outcomes with data models.

Level 6

Fraction Division Rapids — Divide fractions by multiplying by the reciprocal.
Decimal Division Station — Divide decimals by scaling place values and checking the size of the quotient.
Ratio and Percent Observatory — Connect ratios, percents, and proportions to solve scale problems.
Circle Circuit — Find circumference and area using the explicit classroom value π = 3.14.
Solid Shape Workshop — Find volume and surface area of cubes and cuboids.
Data Chart Lookout — Read strip and pie charts to compare, total, and interpret data.