Find the numbers two numbers share. Fill a Venn diagram, watch two frogs hop to the first common landing spot, solve little stories and beat the clock.
Start here. A factor of a number goes into it exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you land on when you hop in equal jumps: the multiples of 3 are 3, 6, 9, 12 and so on.
Common factors and the HCF. Two numbers often share some factors. The factors of 12 and 18 that appear in both lists are 1, 2, 3 and 6. The biggest one, 6, is the highest common factor, or HCF. It is also called the greatest common factor (GCF) or greatest common divisor (GCD).
Common multiples and the LCM. Let one frog hop 4 at a time and another hop 6 at a time. They both land on 12, then 24, then 36. These are common multiples. The first one, 12, is the lowest common multiple, or LCM.
The prime factor Venn diagram. Write each number as a product of primes: 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. Put the primes both numbers share in the middle (2 and 3) and the leftovers on the sides. Multiply the middle to get the HCF: 2 × 3 = 6. Multiply everything, with the shared primes counted once, to get the LCM: 2 × 2 × 3 × 3 = 36.
A handy check. For two numbers, HCF × LCM = the first number × the second number. For 12 and 18: 6 × 36 = 216 and 12 × 18 = 216. Use it to find a missing HCF or LCM.
HCF or LCM? Words like "largest", "greatest", "equal groups", "as big as possible" and "no left over" point to the HCF, because you are splitting things up. Words like "next time", "together again", "every" and "after how many" point to the LCM, because you are waiting for two repeating things to line up.
Simplifying fractions. To write 24/36 in its simplest form, divide the top and the bottom by their HCF, which is 12. You get 2/3, and now 2 and 3 share no factor except 1.
The HCF is the highest common factor: the biggest number that divides two or more numbers exactly. The HCF of 12 and 18 is 6.
The LCM is the lowest common multiple: the smallest number that is a multiple of two or more numbers. The LCM of 4 and 6 is 12.
Write each number as a product of primes, find the primes they share (count repeats carefully), and multiply those shared primes. For 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3 the shared primes are 2 and 3, so the HCF is 6.
Factors are smaller than or equal to the number and divide into it. Multiples are bigger than or equal to the number and come from times tables. 3 is a factor of 12. 24 is a multiple of 12.
Yes. HCF (highest common factor), GCF (greatest common factor) and GCD (greatest common divisor) are different names for the same thing.
Just starting: common factors and hopping frogs with numbers up to 30. I know the basics: HCF and LCM of two numbers up to 40, with prime factors and stories. Challenge me: numbers up to 100, three numbers, simplifying fractions and mixed stories.
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