Prime Time | Mathematics Grade 6 CBSE

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Six ideas about primes

Factors, multiples, primes and the way numbers are built from them. Tap each term to see what it means and how the ideas link up.

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The three big ideas

A factor divides a number exactly (remainder 0). Factors of 12: 1, 2, 3, 4, 6, 12. Every number's smallest factor is 1 and largest is itself.
A multiple is what you get by multiplying: multiples of 7 are 7, 14, 21, 28 … There are endlessly many.
The link: if 3 is a factor of 12, then 12 is a multiple of 3 – two views of the same fact.
Factors come in pairs: for 12, 1×12, 2×6, 3×4 – a quick way to find them all without missing any.

Common mistake: mixing up the two. Factors are smaller-or-equal and there are only a few; multiples are bigger-or-equal and go on forever.

A prime number has exactly two factors – 1 and itself: 2, 3, 5, 7, 11, 13, 17, 19 …
A composite number has more than two factors: 4, 6, 8, 9, 10, 12 …
1 is neither prime nor composite (just one factor). 2 is the only even prime – every other even number is divisible by 2 as well.
Quick divisibility rules: by 2 – last digit even; by 5 – ends in 0 or 5; by 10 – ends in 0; by 3 – digit sum divisible by 3; by 9 – digit sum divisible by 9.
Twin primes are primes just 2 apart: (3, 5), (5, 7), (11, 13).

Common mistake: thinking all odd numbers are prime. 9 is odd but composite (9 = 3×3), and 2 is even yet prime. Count the factors to be sure.

Prime factorisation writes a number as a product of primes only. Every number has exactly one such "fingerprint".
Keep dividing by the smallest prime that fits: 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
HCF (highest common factor) is the biggest number that divides two numbers; LCM (lowest common multiple) is the smallest number both divide into.
Two numbers whose only common factor is 1 are called co-prime (for example 8 and 9).

Worked example. Find the prime factorisation of 60, then use it to find the HCF and LCM of 12 and 18.

Step 1. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.

Step 2. 12 = 2² × 3 and 18 = 2 × 3². The common primes are 2 and 3.

Step 3. HCF = take the lower power of each shared prime: 2 × 3 = 6.

Step 4. LCM = take the higher power of every prime: 2² × 3² = 36.

Where you'll meet it

Primes & factors at work

Sharing into equal groups

Arranging 24 sweets into equal rows only works for a factor of 24 (1, 2, 3, 4, 6, 8, 12, 24). A prime number of sweets, like 23, can only be shared as one big group or singles – factors decide what fits.

Lights, gears & timetables

Two flashing lights or two buses on different gaps line up again at their LCM. The LCM answers "when do these cycles meet?" – from festival lights to train schedules.

Codes & secret messages

Modern internet security multiplies enormous primes together because the product is extremely hard to factor back. The simple idea of prime building blocks keeps online payments safe.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and case studies, testing whether you can use the ideas, not just recall them.

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