Multiples and factors
The first multiples of a number, the multiples between two numbers, every factor found in pairs and the difference between "is a multiple of" and "is a factor of".
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Teaching guide: factors, multiples and divisibility
Factors and multiples are about when one number divides another exactly. In Grades 5 and 6 pupils list multiples and factors, learn the divisibility rules and spot prime numbers; in Grade 7 they write numbers as products of primes and find the HCF and LCM to solve problems. This free generator creates A4 worksheets for every step, with an answer key that shows the division, digit sum or prime factorisation behind each answer.
Student worksheet 
Answer key Divisibility rules
By 2, 5 and 10 from the last digit; by 3 and 9 from the digit sum; by 4 from the last two digits; by 6 and 11 in Grade 7.
7 Prime numbers
Prime or composite up to 50, up to 100 and from 101 to 199, trying the primes until their square is larger than the number.
2² Prime factorisation
The column method (number | prime): divide by the smallest prime until you reach 1, then write the answer with powers, as a factor tree does.
HCF and LCM
First by listing factors and multiples, then by prime factors: the common primes with the lowest power (HCF) or every prime with the highest (LCM).
Word problems
Buses that leave together again, ribbons to cut, bags of sweets or a box full of cubes: pupils decide whether they need the LCM or the HCF.
Frequently asked questions about factors and multiples worksheets
What is the difference between a factor and a multiple?
If 24 = 6 × 4, then 24 is a multiple of 6 and 6 is a factor of 24. A number has endless multiples (6, 12, 18…) but only a few factors (those of 24 are 1, 2, 3, 4, 6, 8, 12 and 24). "Divisible by" means the same as "a multiple of": 24 is divisible by 6.
How do you find all the factors of a number?
In pairs: divide by 1, 2, 3… and every exact division gives two factors, the divisor and the quotient (24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6). Once the divisor is larger than the quotient, you have them all.
What are the divisibility rules?
By 2 if the last digit is even; by 5 if it ends in 0 or 5; by 10 if it ends in 0; by 3 or 9 if its digit sum is; by 4 if its last two digits are; by 6 if it is divisible by 2 and 3; by 11 if the difference between the sums of alternate digits is 0 or a multiple of 11.
How can I tell if a number is prime?
Try dividing by the primes 2, 3, 5, 7, 11… If no division is exact before the square of the prime is larger than the number, it is prime. For 97 you only need to try up to 7, because 11 × 11 = 121 > 97.
How do you work out the HCF and LCM?
Write the numbers as products of prime factors. The HCF is the product of the common primes with the lowest power; the LCM is the product of every prime with the highest power. With 12 = 2² × 3 and 18 = 2 × 3², HCF = 2 × 3 = 6 and LCM = 2² × 3² = 36.
When do you use the LCM and when the HCF in a word problem?
The LCM answers "when will they happen together again" (buses, lighthouses, laps); the HCF answers "the largest possible to share into equal parts" (ribbon pieces, bags, teams). The word problems mix both so that pupils learn to decide.
Which grades are these worksheets for?
Multiples, factors, the rules for 2, 3, 5, 9 and 10 and primes up to 100 are for Grades 5 and 6; prime factorisation, the HCF, the LCM and their word problems for Grades 6 and 7. Afterwards pupils use the HCF and LCM to simplify fractions and find a common denominator.
What other worksheets go well with these?
The times tables for multiples, equivalent fractions and fraction operations, which use the HCF and LCM. Find every resource under maths worksheets.
How do I print only the answer key?
Click Print and choose "Answer key", or "Worksheet and answer key" for both. Your browser's print dialog can also save it as a PDF. Worksheets are generated in your browser and no data is sent anywhere.
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