Divisibility
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الشرح
👀 Let's look
Divisibility, G.C.F and L.C.M. A few rules save all the dividing.
Look at the last digit, or add the digits up.
What "divisible" means
One number is divisible by another when the division comes out exactly, with nothing left over. 12 is divisible by 3, because 12 ÷ 3 = 4 exactly. It is not divisible by 5, because 12 ÷ 5 leaves 2 behind.
You can answer that without dividing at all. Each small number leaves a mark you can read off the number itself — some in the last digit, some in the sum of all the digits.
The five rules
Divisible by 2 — the last digit is even (0, 2, 4, 6, 8).
Divisible by 5 — the last digit is 0 or 5.
Divisible by 10 — the last digit is 0.
Divisible by 3 — the digits add up to a multiple of 3.
Divisible by 9 — the digits add up to a multiple of 9.
Two of these come free. Anything divisible by 10 is divisible by 2 and by 5 as well, and anything divisible by 9 is divisible by 3 — so a digit sum of 9 answers both questions at once.
126
2✓last digit is even
3✓digits add to 9
5✕last digit is 0 or 5
9✓digits add to 9
10✕last digit is 0
Testing every rule in turn.
أمثلة محلولة
Worked exampleTesting 126
Which numbers divide 126 exactly?
Worked exampleTesting 405
Which numbers divide 405 exactly?
Worked exampleTesting 250
Which numbers divide 250 exactly?