PredictionFractionsEasy
The Number 37 Secret
Repeat any digit three times, divide by its triple — you always land on 37.
Worked demonstration
Pick any single digit from 1 to 9. Write it three times in a row to make a three-digit number (for example 3 becomes 333). Now add your digit to itself three times to get its triple (for example 3 + 3 + 3 = 9). Divide the three-digit number by that triple. What number do you get?
Try it yourself
Why it works
A digit written three times is that digit × 111, and 111 = 3 × 37, so dividing by three times the digit always leaves 37.
Background & Explore Further
This is the same digit-cancellation idea behind 'casting out nines' error checks, and it springs from repunits — numbers like 111 made of repeated 1s. Explore why 111 = 3 × 37 and what other repunits factor into.
Maths Made Magic — Queen Mary University of London (cs4fn)