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MrV’s Shorthand Division (by Single Digits 2, 5, and 3) It Helps You Do Prime Factorization using Factor Trees: If you are SURE that a long number divides exactly by 2, 5, or 3, you can use Shorthand Division to quickly find the other factor. Easy Tests for Divisibility: 2: Only even numbers (ending with 0, 2, 4, 6, or 8) divide by 2 Examples: 34,138 will divide by 2, but 123,243 will not 5: Only numbers ending with 0 or 5 will divide by 5 Examples: 3,005 will divide by 5, but 3,002 will not 3: Only numbers with a digit sum that divides by 3 also divide by 3 Examples: 15,201 will divide by 3, but 15,202 will not 1+5+2+0+1=9 1+5+2+0+2=10 7: There’s no easy test - Divide by 7 (use either kind of division) to see if you get a 0 remainder 4, 6, 8, and 9: Why bother? Check for the primes first. If 2 and 3 will not divide, then these other digits will not How to do Shorthand Division • Let’s use 6408 divided by 2 as an example… • Write the division with the division symbol upside down, and build the quotient underneath it --> 2)6408 quotient • Work left to right, one digit at a time 2 into 6 is 3 2 into 4 is 2 2 into 0 is 0 2 into 8 is 4 2)6408 2)6408 2)6408 2)6408 3 32 320 3204 • It’s easy if each little division goes evenly. But if not… ? • Let’s call any remainders “carries.” (They get carried to the next digit) 2 into 7 is 3, r1 2 into 12 is 6 2 into 1 is 0 r1 2 into 18 is 9 2 ) 7 12 1 8 3 2 ) 7 12 1 8 36 2 ) 7 12 1 18 360 2 ) 7 12 1 18 3 609 • Many students can do these little divisions in their heads, but some may find MrV’s Tables are useful when dividing by 3, 5 and 7 Long Division compared to Shorthand Division • Dividing a number by 2: Either it goes exactly, or there is a remainder of 1 • You can use MrV’s Times Table. You may find it easier if you do some computations in your head • Long Division: 436 , 029 2 872 , 058 8 07 6 12 12 00 0 04 4 0 Shorthand Division: (leave some space between the digits) 1 1 8 7 2, 0 5 8 2 4 3 6, 0 2 9 5 7 2 into 8 goes 4, exactly 2 into 7 goes 3, with 1 left over – making the next digit 12 2 into 12 goes 6, exactly 2 into 0 goes 0, exactly 2 into 5 goes 2, with 1 left over – making the next digit 18 2 into 18 goes 9, exactly Long Division compared to Shorthand Division • Dividing a number by 3: Either it goes exactly, or there is a remainder of 1 or 2 • You can use MrV’s Times Table. You may find it easier if you do some computations in your head • Long Division: Shorthand Division: (leave some space between the digits) 21 , 409 3 64 , 227 6 04 3 12 12 02 00 27 27 0 1 2 6 4, 2 2 7 3 2 1, 4 0 9 2 4 3 into 6 goes 2, exactly 3 into 4 goes 1, with 1 left over – making the next digit 12 3 into 12 goes 4, exactly 3 into 2 goes 0, with 2 left over – making the next digit 27 3 into 27 goes 9, exactly