Factors and Multiples Worksheet for Class 5 — Free UP Board PDF with Answers

This factors and multiples worksheet for Class 5 follows the UP Board and NCERT Class 5 maths syllabus and gives students 30 free practice questions covering factors, multiples, prime and composite numbers, divisibility rules, HCF (highest common factor), and LCM (lowest common multiple). Every question has a full answer key in the printable PDF.

Factors and multiples are two sides of the same coin. A factor of a number divides it exactly with no remainder. A multiple of a number is what you get when you multiply it by any counting number. For example, 1, 2, 3, 4, 6 and 12 are factors of 12, while 12, 24, 36, 48 and 60 are multiples of 12. Class 5 students need to be fluent with both ideas — they are the foundation for HCF and LCM in Class 6 and 7.

This free worksheet for Class 5 splits questions across easy, medium, and hard difficulty. Easy questions test direct recall of factors and multiples, medium questions add prime numbers and divisibility rules for 2, 3, 5, 9 and 10, and hard questions include word problems and introductory HCF and LCM.

A factor of a number divides that number exactly — nothing left over. Every number has at least two factors: 1 and itself. Some numbers (called prime numbers) have only these two factors. Others (composite numbers) have more.

Example: Find all factors of 24. We check each number from 1 upwards: 1 × 24 = 24, 2 × 12 = 24, 3 × 8 = 24, 4 × 6 = 24. So the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 — eight factors in total. A simple way to list them is to pair them up as we find them.

Example: Find all factors of 13. We try: 1 × 13 = 13, 2 doesn't divide 13, 3 doesn't either, and so on until we hit 13 itself. Only 1 and 13 divide 13 exactly. So 13 is a prime number — it has only two factors.

The multiples of a number are the results of multiplying it by 1, 2, 3, 4, and so on. Multiples go on forever. Every number is a multiple of itself and also of 1.

Example: First five multiples of 6 are 6, 12, 18, 24 and 30 — obtained by 6 × 1, 6 × 2, 6 × 3, 6 × 4, 6 × 5. The eighth multiple of 6 is 6 × 8 = 48.

Example: Is 42 a multiple of 7? Check by dividing: 42 ÷ 7 = 6 with no remainder. Yes, 42 is the 6th multiple of 7. Knowing your multiplication tables up to 10 makes these questions very quick for Class 5 students.

Instead of actually dividing, divisibility rules let you check at a glance whether one number divides another. These rules appear in nearly every factors and multiples worksheet for Class 5 and are worth memorising.

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8 (so every even number). It is divisible by 3 if the sum of its digits is a multiple of 3 (for example 126 → 1+2+6 = 9, which is a multiple of 3, so 126 is divisible by 3). It is divisible by 5 if the last digit is 0 or 5. It is divisible by 9 if the sum of digits is a multiple of 9. And it is divisible by 10 if the last digit is 0. These five rules handle most Class 5 questions.

HCF (Highest Common Factor) is the biggest number that divides two or more numbers exactly. LCM (Lowest Common Multiple) is the smallest number that is a multiple of two or more numbers. Class 5 introduces both ideas using the listing method.

Example HCF: Find HCF of 12 and 18. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. HCF = 6 (the biggest one).

Example LCM: Find LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24. Multiples of 6: 6, 12, 18, 24, 30. Common multiples: 12, 24. LCM = 12 (the smallest one).

The worksheet PDF includes 8 practice questions on HCF and LCM at this level — perfect preparation for the longer prime-factorisation method students meet in Class 6.