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Lesson 1 of 16

What a digit sum remembers

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6 min

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Write 4321. Under it, write its digit sum. That is the total of its digits: 4 + 3 + 2 + 1 = 10.

4321. Add its digits: 4 + 3 + 2 + 1 = 10.
Step 1 of 4
  1. 4321. Add its digits: 4 + 3 + 2 + 1 = 10.
  2. 4321 ÷ 9 leaves 1 over. 10 ÷ 9 leaves 1 over too.
  3. 4321 ÷ 3 leaves 1 over. 10 ÷ 3 leaves 1 over too.
  4. Same leftover, both times, on 9 and on 3.

Same leftover, both times

The amount left over after dividing is the leftover. For example, 10 ÷ 9 leaves 1.

Add up a number's digits. Divide the number by 9, and divide the digit sum by 9. Both divisions leave the same amount over. The same is true for 3.

A digit sum can still be big. Add its digits again. The digit sum of 918 is 9 + 1 + 8 = 18. Add again: 1 + 8 = 9. Each round makes a smaller number. So the rounds always stop at one digit. On 9 and on 3, the leftover stays the same each round.

Pick a number and 9 or 3. Watch the lab divide the number and its digit sum. Check the two leftovers match.

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Try the lab to finish this lesson.