Divisibility Dreams www.MaxLearning.Net 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. Topic Text Video Divisibility Dreams Reference Sheets (3 across) Cut out and keep one of these with you until you memorize each rule. A number is exactly divisible by: 2 If it is even (ends in 0, 2, 4, 6, 8) . 3 If its SOD (Sum Of Digits) is divisible by 3 [546: 5+4+6 = 15]. 4 If it is even and its last 2 digits = 00  or are divisible by 4 . 5 If it ends in 0  or 5 . 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). 8 If it is even and its last 3 digits = 000  or are divisible by 8  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 . 11 If SOD(odd) – SOD(even) = 0  [572: (5+2) – 7 = 7 – 7 = 0] or is divisible by 11  [2816: (2+1) – (8+6) = 3 – 14 = -11]. 12 If it follows rules for both 4 and 3 [924: 9+2+4 = 15].