5. Prime Time

8 topics1 h

Chapter 5 of NCERT Mathematics for Class 6: Prime Time. Four sections — Multiples and factors held in common, Primes, Co-primes and prime factorisation and Shortcuts and explorations. Eight videos, 1 h in all.

Worked answers to the 42 exercise questions in this chapter →

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Part 1

Multiples and factors held in common

11 minCommon multiples: why the first "idli-vada" is 15Why does the FIRST “apple-banana” land on 15 — and why does the pattern break for 4 and 6?11 min · 12 partsहिंदी10 minCommon factors: which jump sizes can land on a numberWhich jump lengths land exactly on 24 — and why do 14 and 36 share almost nothing?10 min · 12 partsहिंदी

Part 2

Primes

11 minPrime and composite: the rectangle test for a number's factorsTwelve figs pack into three different rectangles. Seven pack into one. That difference has a name.11 min · 12 partsहिंदी10 minThe sieve of Eratosthenes: finding primes by removing multiplesTwenty-five primes below 100, found without a single division. The sieve never tests anything — it only deletes.10 min · 12 partsहिंदी

Part 3

Co-primes and prime factorisation

11 minCo-prime pairs, and why sharing no factor is what matters4 and 9 are co-prime, and neither one is prime. The name is a trap — and the fix is three pictures of one fact.11 min · 12 partsहिंदी10 minPrime factorisation, and why there is only one of them per numberA student's arithmetic is perfectly correct and her conclusion is wrong. The fix is to stop splitting once and keep splitting.10 min · 12 partsहिंदी8 minReading co-primality and divisibility straight off the prime factorisation42 has every prime that 12 has, and 12 still doesn't divide it. Counting the copies is the half everyone drops.8 min · 12 partsहिंदी

Part 4

Shortcuts and explorations

11 minDivisibility tests for 10, 5, 2, 4 and 8: why only the last digits matterFive divisibility shortcuts that look like five tricks. They are one trick, and it is a fact about how we write numbers.11 min · 12 partsहिंदी

What you will be able to do

  • Decide, for any number, which of two counting rhythms land on it
  • List every factor of a number under 100 systematically, in pairs
  • Build every rectangular arrangement of a given number of objects, and read a factor pair off each one
  • Carry out the printed procedure on a hundred grid and produce the primes below 100
  • State the definition: a pair sharing no factor above 1
  • Explain why one factorisation of a number does not reveal all its factors
  • Decide whether two numbers are co-prime by comparing their prime factorisations
  • Test a number for divisibility by 10, 5 and 2 from its last digit

What this chapter assumes you already know

  • Skip-counting in threes, fives and tens from primary school
  • The word multiple: the numbers you reach by counting in steps of a fixed size
  • Reading a two-circle overlap diagram — which region means "both"
  • Multiplication tables up to 10, well enough to recognise a multiple on sight
  • Division with remainder, and recognising a remainder of zero as "goes exactly"
  • Multiplication tables to 10, well enough to spot a factor pair
  • Reading a number line and marking equally spaced points on it
  • Skip-counting from 0 rather than from 1 — the jumps in this topic start at 0

It builds directly on Every number sequence is a rule, not a list.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "15 is first because 15 is a special number."
  • "Common multiples run out."
  • "The overlap region means 'either'."
  • "To count the double calls up to 90 I have to write the game out."
  • "Every multiple of the second number should give a lone second call."
  • "The first common multiple is always the two numbers multiplied."
  • "1 and the number itself do not really count as factors."
  • "Common factors of a big pair should be a long list."