concepts · 16
- 01
The Biggest Tile That Fits
Find the biggest square tile that covers a 12 ft by 16 ft floor exactly, and meet the Highest Common Factor (HCF).
- 02
Rice Bags And Jump Jackpot
Pack rice from two farms in equal bags using as few bags as possible, and find the longest jump that lands on two treasures.
- 03
Prime Factorisation
Break any number into primes with a factor tree or the division method, and see why you always get the same primes.
- 04
Every Factor From Prime Factors
Build every factor of a number from its prime factors, and learn how one counterexample can break a claim.
- 05
Common Factors From Prime Factors
Find all the common factors of two numbers by spotting the subparts their prime factorisations share, then pick the biggest.
- 06
The HCF Shortcut
Find the HCF directly: take each prime the numbers share, the fewest times it appears. Works for three numbers too.
- 07
Torans, Gajak And The LCM
Find the shortest toran two people can both make, and the next day for free gajak, and meet the Lowest Common Multiple (LCM).
- 08
The LCM From Prime Factors
A multiple contains the whole prime factorisation of the number. Build the LCM by taking each prime the most times it appears.
- 09
Patterns And General Statements
Turn examples into rules that always hold, such as 'if one number divides the other, it is their HCF', and write them with algebra.
- 10
What Happens When Numbers Are Doubled
Double both numbers and the HCF doubles. Find out when the HCF of two multiples of the same number is exactly that number.
- 11
One Ladder For HCF And LCM
Divide two numbers by common factors in one ladder and read off both the HCF and the LCM, then speed it up with bigger divisors.
- 12
HCF × LCM = Product
Discover that the HCF times the LCM of two numbers is their product, see why, and use it to find a missing value.
- 13
HCF Word Problems: Cubes In A Box
Decide which cube sizes pack a box with no gaps, and find the biggest number that divides two numbers.
- 14
LCM Word Problems: Stars, Cows And A Circle Game
Find when repeating patterns line up, how many cows the cowherd had, and how many children were playing Fire in the Mountain.
- 15
Two Challenges: The Dog And The Rabbit, And Mahaviracharya's Fractions
Work out when a dog catches a rabbit with a head start, and add five fractions from Mahaviracharya using the LCM.
- 16
Review: Finding Common Ground
Check what you can now do with factors and multiples, revise the HCF and LCM rules, and decode the book's mystery colours.