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Divisibility Dreams www.MaxLearning.Net |
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Any number is divisible by any other number (except zero). But when you need to know if a number is exactly divisible (with no remainder) by another, the following rules can tell you without having to actually perform the division. This makes it a dream when your task is to factor a larger number into its smaller multipliers. |
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Text |
Video |
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Divisibility Dreams Reference Sheets
(3
across) Cut out and keep one of these with you until you memorize each rule. |
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| A number is exactly divisible by: | |||
| 2 | If it is even (ends in 0, 2, 4, 6, 8) [976]. | ||
| 3 |
If its SOD (Sum Of Digits) is divisible by 3 [546: 5+4+6 = 15]. |
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| 4 | If it is even and its last 2 digits = 00 [300] or are divisible by 4 [316]. | ||
| 5 | If it ends in 0 [230] or 5 [765]. | ||
| 6 | If it follows rules for both 2 and 3 [462: 4+6+2 = 12]. | ||
| 7 |
If its
1st digit/s
minus twice its
last digit
= 0 [147:
14
– (2×7)
= 14 – 14 = 0] or
is divisible by 7 [91:
9
– (2×1)
= 9 – 2 = 7]. * To seek 7 is futile (first minus twice last). |
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| 8 | If it is even and its last 3 digits = 000 [5000] or are divisible by 8 [3888] or twice the first two of the 3 digits plus the last is divisible by 8 [3152: (2×15) + 2 = 30 + 2 = 32]. * He ate(8) & was too full (twice first plus last). | ||
| 9 | If its SOD (Sum Of Digits) is divisible by 9 [2754: 2+7+5+4 = 18]. | ||
| 10 | If it ends in 0 [6370]. | ||
| 11 |
If SOD(odd)
– SOD(even)
= 0 [572:
(5+2)
–
7
= 7 – 7 = 0] |
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| 12 | If it follows rules for both 4 and 3 [924: 9+2+4 = 15]. | ||
