Start with the meaning
NCERT connection: Grade 6 Ganita Prakash, “Prime Time”. These are independent BananaLearn notes and original practice, not official NCERT material or a complete set of textbook exercise solutions. Match the chapter name to the book used by your school. Start with multiplication facts and exact whole-number division. This guide focuses on positive integers and selected chapter skills, not every activity in the book.
Find factors by making complete pairs
A positive factor divides a number with no remainder. To list the factors of 24, write 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Both numbers in each pair belong in the factor list.
Once the smaller number passes the larger number, later pairs repeat earlier ones. List the factors in order: 1, 2, 3, 4, 6, 8, 12, 24. Do not stop after finding only the small factors.
Keep factors and multiples apart
Factors of a positive integer form a finite list. Positive multiples keep going: the positive multiples of six start 6, 12, 18, 24, 30. Each is six multiplied by a positive whole number.
Ask which number is being divided. In “Is 8 a factor of 40?”, calculate 40 ÷ 8. In “Is 40 a multiple of 8?”, the same exact division establishes the relationship.
Prime is different from co-prime
A prime number has exactly two positive factors: one and itself. One has only one positive factor, so it is not prime. Two is prime and is the only even prime.
Co-prime describes a pair whose only common positive factor is one. Eight and fifteen are co-prime even though both are composite. Being co-prime does not mean that both numbers must be prime.
Break a number into prime factors
Split 60 into 6 × 10, then split 6 into 2 × 3 and 10 into 2 × 5. The result is 2 × 2 × 3 × 5. Every remaining factor is prime.
A different first split, such as 12 × 5, leads to the same prime factors apart from order. Multiply the final factors to check that they reconstruct 60. A factor tree ending in a composite number is unfinished.
Worked examples, step by step
Example 1: List every positive factor of 30
- Write factor pairs: 1 × 30, 2 × 15, 3 × 10, 5 × 6.
- Collect both entries from each pair: 1, 2, 3, 5, 6, 10, 15, 30.
- Check that each listed number divides 30 without a remainder.
Example 2: Are 14 and 25 co-prime?
- Factors of 14 are 1, 2, 7, 14; factors of 25 are 1, 5, 25.
- Their only common positive factor is 1.
- They are co-prime; neither needs to be a prime number.
Example 3: Prime-factorise 84
- 84 = 12 × 7, and 12 = 3 × 4.
- Split 4 into 2 × 2: 84 = 2 × 2 × 3 × 7.
- All four factors are prime, and their product is 84.
Common mistakes and useful repairs
Calling 1 a prime number
Count its positive factors. Only 1 divides 1, so it does not have the two different factors required for a prime.
Assuming every odd number is prime
Nine is odd but 9 = 3 × 3. Try factor pairs instead of using oddness as proof.
Try before revealing
Quick understanding check
Read the check answers
23. 23 has no positive factors other than 1 and 23.
8 and 15. Eight and fifteen share only the positive factor 1.
Grade 6 Prime Time: factors, multiples and prime numbers — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
List the positive factors of 18.
Show answer and reasoning
1, 2, 3, 6, 9, 18. Use the pairs 1 × 18, 2 × 9 and 3 × 6.
Write the first five positive multiples of 7.
Show answer and reasoning
7, 14, 21, 28, 35. Multiply 7 by 1, 2, 3, 4 and 5.
Is 39 prime or composite?
Show answer and reasoning
Composite. 39 = 3 × 13, so it has factors other than 1 and 39.
Prime-factorise 72.
Show answer and reasoning
2 × 2 × 2 × 3 × 3. 72 = 8 × 9 = (2 × 2 × 2) × (3 × 3).
Are 9 and 20 co-prime?
Show answer and reasoning
Yes. The factors of 9 are 1, 3, 9; none except 1 divides 20.
List the common positive factors of 16 and 24.
Show answer and reasoning
1, 2, 4, 8. Check each factor of 16 against 24.
Give an even prime and an odd composite number.
Show answer and reasoning
2 and 15, for example. Two has exactly two positive factors; fifteen has the extra factors 3 and 5.
Can 6 be both a factor and a multiple? Give examples.
Show answer and reasoning
Yes: a factor of 24 and a multiple of 3. 24 = 6 × 4, while 6 = 3 × 2. The relationship depends on the other number.
Grade 6 Prime Time: factors, multiples and prime numbers — worked answer key
1, 2, 3, 6, 9, 18. Use the pairs 1 × 18, 2 × 9 and 3 × 6.
7, 14, 21, 28, 35. Multiply 7 by 1, 2, 3, 4 and 5.
Composite. 39 = 3 × 13, so it has factors other than 1 and 39.
2 × 2 × 2 × 3 × 3. 72 = 8 × 9 = (2 × 2 × 2) × (3 × 3).
Yes. The factors of 9 are 1, 3, 9; none except 1 divides 20.
1, 2, 4, 8. Check each factor of 16 against 24.
2 and 15, for example. Two has exactly two positive factors; fifteen has the extra factors 3 and 5.
Yes: a factor of 24 and a multiple of 3. 24 = 6 × 4, while 6 = 3 × 2. The relationship depends on the other number.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to Division: sharing equally and making equal groups before trying a fresh problem.
Help at home: Ask for a factor pair, not a guess
Choose 24 counters. Ask your child to arrange them into complete rectangular arrays and record both dimensions of each array. Connect the dimensions to factor pairs.
If they miss a factor, ask which partner would multiply with it to make 24. If they confuse factors with multiples, keep the fixed total visible throughout the activity.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Are these NCERT exercise solutions?
No. These are original questions with worked answers that support the named topic. Use the official textbook link for the book itself. Exercise numbers and school sequences can differ between editions.
How should a parent use the practice?
Ask for one independent attempt before revealing an answer. Notice whether the difficulty is reading the question, representing the idea or calculating. Revisit the matching example, then try a fresh question rather than copying the worked answer.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
Bring the sticking point to a teacher
For 1-on-1 support, bring one question your child found difficult to a free 50-minute session. Tell us their grade, curriculum and time zone so we can discuss a suitable next step.
Request a free session