Number Properties: Common Factors and Multiples

Methods in this video

Tap a time to jump to where the video teaches that method.

1. 1

   Half the key must divide every value

   ▶ 1:00

   When to use it: A picture graph may use only whole symbols and half symbols, never any other part (whole and half … no other fractions / a row may end with half a symbol), and the question asks which keys can be used, or the largest number one whole symbol could stand for.

   • Divide the key by 2 first: half the key must divide every value, and if one value fails, the key cannot be used.
   • Check every value; checking only some leads to the wrong answer. When the question asks for the largest, check from the biggest down.
   • Judge a key by its half, not by itself: a key that divides none of the values exactly can still work.
   • For a faster way, break each number into primes and multiply the ones they all share: that is the highest common factor (HCF).
2. 2

   List the biggest, check the rest

   ▶ 6:49

   When to use it: Several things each repeat at their own interval (every 8 minutes, every 3rd day, flashing, buses leaving, runners back at the start line), and the question asks when they are next together, or the first time after a given time when they coincide; or a number must be a multiple of several numbers at once. No candidates are handed to you to check.

   • To find when things are together again, list multiples of the biggest number and check each one with the rest; the first that works for all of them is the answer.
   • It must work for every number; one that fits only two of them is the trap.
   • If they don't start together, find the first time they actually meet, then jump forward by the shared step.
   • For a faster way, break each number into primes and multiply the most copies of each prime: that is the lowest common multiple (LCM).