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Section 1.5 · Number

Tests for divisibility

Use tests of divisibility to check whether one number divides exactly into another.

6 teaching slides 54 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

divisibleOne number is divisible by another when the division leaves no remainder.
tests of divisibilityQuick checks that tell you whether one number divides exactly into another.
remainderWhat is left over after a division.
digit sumThe total you get by adding all the digits of a number.
consecutiveNumbers that follow each other in order, such as 7, 8, 9.

3 · Summary of the sectionrevise from this

  • ÷ 2 — the last digit is even
  • ÷ 3 — the sum of the digits is divisible by 3
  • ÷ 4 — the number formed by the last two digits is divisible by 4
  • ÷ 5 — the last digit is 0 or 5
  • ÷ 6 — it passes the tests for both 2 and 3
  • ÷ 8 — the number formed by the last three digits is divisible by 8
  • ÷ 9 — the sum of the digits is divisible by 9
  • ÷ 10 — the last digit is 0
  • ÷ 11 — the difference between the sum of the odd-position digits and the sum of the even-position digits is 0 or a multiple of 11
  • You can combine tests when the two divisors share no factors: a number divisible by 3 and by 4 is divisible by 12. But 2 and 4 do share a factor, so passing both does not guarantee divisibility by 8.
PDFPrintable worksheet All 54 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons3 videos

Divisibility Rules (2, 3, 4, & 5)

American Math with Mr. J

Clear rules and examples for the easiest divisibility tests.

Divisibility Rules (6, 7, 8, 9, & 10)

American Math with Mr. J

The remaining tests, including the digit-sum rule for 9 and the combined rule for 6.

All the Divisibility Tests You Need for Maths Challenges

British stretchKevin Olding – Mathsaurus

A British presenter runs through every standard test and explains why each one works.

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4 · Practice54 questions, easiest first

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1.4 Highest common factors
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1.6 Square roots and cube roots