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1Place Value to Billions2Roman Numeral Arithmetic3Twin Primes & Co-primes4Divisibility Rules5Cryptarithm Puzzles6Estimation of Products7Division Cryptarithms

Concept 3 of 7

Twin Primes & Co-primes

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Today's big idea

Twin primes are both prime and 2 apart, while co-primes need only share no factor.

Co-prime says nothing about being prime, since 8 and 9 share no factor at all.

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How it works

👀 What's going on?

Two numbers can be close in two very different ways, and the words for those ways sound alike enough to swap by accident. One is about being prime; the other is not.

💡 Here's the trick

Twin primes · Co-primesTwin primes3,55,711,1317,19Both prime · differ by 2Co-prime (HCF = 1)8,159,1625,36No common prime factorAll twin primes are co-prime; not all co-primes are prime

Look at the pairs above. Twin primes are both prime and exactly 2 apart. Co-prime is a weaker idea altogether: the two simply share no factor beyond 1, and neither of them has to be prime.

🪄 How to do it

  1. 1.Read the pairs above and ask whether both numbers are prime.
  2. 2.For twin primes, check the gap is exactly 2.
  3. 3.For co-primes, work out the HCF and check it is 1.

✍️ Try it

Are 29 and 31 twin primes? Then: are 14 and 15 co-prime?

Both 29 and 31 are prime and they differ by 2, so yes, they are twin primes. 14 is 2 times 7 and 15 is 3 times 5, sharing nothing, so yes, they are co-prime even though neither is prime.

⚠️ Watch out

You might be thinking co-prime numbers must themselves be prime. They need not be. 8 and 9 share no factor at all, while 3 and 9 are not co-prime even though 3 is prime.

🌟 Why this matters

A fraction sits in its lowest terms exactly when its top and bottom are co-prime. That is how you know when to stop simplifying, and it saves you cancelling a fraction that will not go any further.
Exam tip: Find the HCF first, since 1 settles it.

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Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Which pair is co-prime: (14, 21) or (15, 28)?”

  1. 1

    Find HCF of (14, 21)

    Both share 7 → HCF = 7 → NOT co-prime.

  2. 2

    Find HCF of (15, 28)

    15 = 3 × 5, 28 = 2² × 7 → no common prime → HCF = 1.

  3. 3

    Identify

    HCF = 1 means co-prime ✓.

  4. 4

    Answer ✓

    (15, 28) is co-prime

Now you try one — same steps, different story 👇

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See it in action

⚡ Time to play!

Co-prime numbers share no factor except 1 (HCF = 1). Twin primes are two primes that differ by 2.

PAIRS · ROUND 1 OF 3

Which pair is CO-PRIME (HCF = 1)?

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Quick check

✅ VERIFICATION

Which pair below is NOT co-prime?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Divisibility Rules

Digit sum, last digit, last two digits, instant tests.

Concept 4 of 7 →