CBSE Class 6 · Mathematics
Prime Time
Official NCERT chapter from Ganita Prakash (book code fegp1). ExamMaster notes are original teaching at CBSE Class 6 depth.
This lesson follows the official chapter “Prime Time” in Ganita Prakash. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 6
- Easy level
- 8 concepts
1Common Multiples and Common Factors
A common multiple of 4 and 6 lands on both skip-counts: 12, 24, … A common factor divides both: 1 and 2 for 4 and 6 (and more if they share others).
A multiple of only one number is not common.
Figure. Factors of 12 and 18 split into only-12, shared, and only-18. The largest shared box is 6, the HCF. 36 is the first common multiple, named under the columns, not guessed.
How it works
- List a few multiples (or factors) of AEvidence.
- List the same kind for BEvidence.
- Keep the overlapCommon.
2Prime Numbers
A prime has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are primes. 9 = 3×3 is not.
“Looks lonely” is not the test.
Figure. A prime is a number whose factor count is exactly two. The dashed rule sits at 2. Bars on the rule are 2, 3, 5 and 7; taller bars are composite.
How it works
- List factors of nArrays that tile n.
- Count distinct factorsExactly two?
- If yes, name prime; if more, composite (for n>1)The test.
3Co-prime numbers for safekeeping treasures
Two numbers are co-prime if their only common factor is 1. 8 and 9 are co-prime; 8 and 12 are not (common 4).
Both being prime is enough but not required: 8 and 9 work.
Figure. 8 and 9 share no prime. Coprime means HCF 1, not that the numbers look small. The empty middle is the treasure lock: two factor lists that do not meet.
How it works
- List common factorsThe overlap.
- If the overlap is only 1, they are co-primeSafe-sharing in this story means no shared factor but 1.
- If a larger common factor exists, they are not co-prime4 kills 8 and 12.
Co-prime or not
Are 15 and 28 co-prime? Are 15 and 25?
- 15 factors1,3,5,15
- 28 factors1,2,4,7,14,28
- 15 and 28only 1 — co-prime
- 15 and 25common 5 — not
Pro tip. Only 1 in the overlap means co-prime.
4Prime Factorisation
Write n as a product of primes: 84 = 2^2 \times 3 \times 7. Factor trees or repeated division by primes both work if every leaf is prime.
Stopping at 4×21 is not finished — 4 and 21 are not prime.
Figure. Divide 84 by 2, then 42 by 2, then 21 by 3, and stop at prime 7. The left column is the unique prime writing, except for order: 2 squared times 3 times 7.
How it works
- Divide by the smallest prime that fits2 if even.
- Repeat on the quotientUntil all prime.
- Write the product of primesUsually with powers.
5Divisibility Tests
A test is a digit-rule you can run: even means last digit even; last digit 0 or 5 for 5; digit-sum for 3 and 9. The test names a rule; it does not guess.
A “feels divisible” is not a test.
Figure. The test for 3 is a named sum, not a guess. Digits of 246 add to 12, then 3. Because 3 divides that sum, 3 divides 246.
How it works
- Name the divisor2, 3, 5, 9, 10…
- Run the matching digit-ruleLast digit, or digit-sum.
- Then, if needed, check by divisionThe test predicts; division confirms.
6A prime has exactly two factors: 1 and itself
That sentence is the definition. 2 is prime (1 and 2). 4 has 1, 2, 4 — three factors, not prime.
Do not add “odd” to the definition: 2 is even and prime.
Figure. Seven has the pair 1 and 7. Eight has 1, 2, 4 and 8. Prime means the factor list has length two, not that the number looks lonely.
How it works
- Count distinct factorsThe definition.
- Allow 2 as the even primeIt passes.
- Reject 1 (next idea) and compositesWrong factor-count.
71 is not a prime
1 has only one distinct factor: itself. The definition asked for two. So 1 is neither prime nor composite.
Calling 1 prime “to be nice” breaks every later unique-factor theorem you will meet.
Figure. 1 has only itself on the factor list. 2 has two names and is prime. 4 has three and is composite. One factor is why 1 is neither prime nor composite.
How it works
- List factors of 1Only 1.
- Count themOne, not two.
- Refuse the name primeAnd refuse composite.
8A test names a rule; it does not guess
“Divisible by 3 because I like 3” is a guess. Digit-sum 18 is a rule for 3 (1+8=9, 9=3×3).
If you cannot name the rule, you did not run a test.
Figure. Divisibility by 2 reads the last digit. 4 is even, so 2 divides 34. 5 is odd, so 2 misses 35. The test names that rule; it does not guess from the look of the whole number.
How it works
- State the rule in a sentenceThe test.
- Apply it to the digitsEvidence.
- Conclude pass or failNot a vibe.
1 is
- Neither prime nor composite
- The first prime
- A composite
Exactly one factor. Prime needs two.
Notes
- The official chapter title is “Prime Time”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- Prime: exactly two distinct factors, 1 and n (n>1).
- 1 is not prime.
- Co-prime: \mathrm{hcf}(a,b)=1.
- Divisibility by 3: digit-sum is a multiple of 3.
Recap
Hold these pegs from the official chapter “Prime Time”. The wording is ExamMaster’s teaching, not a textbook recap.
- Common Multiples and Common Factors
- A common multiple of 4 and 6 lands on both skip-counts: 12, 24, … A common factor divides both: 1 and 2 for 4 and 6 (and more if they share others).
- Prime Numbers
- A prime has exactly two distinct factors: 1 and itself.
- Co-prime numbers for safekeeping treasures
- Two numbers are co-prime if their only common factor is 1.
- Prime Factorisation
- Write n as a product of primes: 84 = 2^2 \times 3 \times 7.
- Divisibility Tests
- A test is a digit-rule you can run: even means last digit even; last digit 0 or 5 for 5; digit-sum for 3 and 9.
- A prime has exactly two factors: 1 and itself
- That sentence is the definition. 2 is prime (1 and 2). 4 has 1, 2, 4 — three factors, not prime.
Practise Prime Time
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device