Multiplying by 14443
Multiplication by 14443 using 101101
My first instinct when tackling the number 14443 was to figure out why the number 14443 was so special. The first observation was that when 14443 is multiplied by a multiple of 7, the answer is always in the form of n0nn0n, under certain circumstances.
In general, the problem 14443 Ã— t = n0nn0n, where t = 7n , the multiple of 7, and 7 t 69. We require these bounds to be put on t for the product to be a six-digit number. 17
14443 Ã— 42 =
Since 42 = 7(6) and thus a multiple of 7, we can simply write the product as 606606.
14443 Ã— 42 = 606606.
That's a great little trick and it will work about of the time! We needed something a little more powerful and a trick that could be used on the other numbers. The thing to notice about the number 14443 is that it is equal to . Remembering how to multiply by 25 led me to nd this trick. When multiplying by 25, you multiply by 100 and divide by 4 because . Why not try that here? The trick to multiplying by 14443 is to multiply the two-digit number by 101101 first and divide by 7.
What does a two-digit number, when multiplied by 101101, look like? It's pretty easy to visualize actually. Think of the number in three different parts. When you multiply 14443 Ã— N and N is a two-digit number, the three parts are
[ N ] [11 N ] [ N ]
14443 Ã— 34 =
To start 14443 Ã— 34, you think 34 374 34, because 34 Ã— 101101 = 3437434.
The next step is to divide by 7, which you should be able to do. Be careful and watch the carries.
Multiplication by 14443 using 13
Further investigation of the number 14443 reveals that it is composite and has a prime factorization of 11 Ã— 13 Ã— 101. Multiplication by 11 and multiplication by 101 are two of the cornerstone tricks for Number Sense. Multiplication by 13 is a little more difficult, but managable. To simplify things even more, the product of 11 and 101 is 1111, which is another easy trick to use.
To multiply by 14443, use the following steps:
14443 Ã— 32 =
Therefore, 14443 Ã— 32 = 462176.
Multiplication by 14443 using quotients and remainders
For the problem 14443 Ã— n , use the following steps: [Work from right to left, step to step.]
14443 Ã— 31 =
Thus, 14443 Ã— 31 = 447733.