Shrinking Number Method

Shrinking Number Method This method is to check the divisibility of a number (dividend) by a number (divisor). This method continuously shrinks the number to be checked for the divisibility using a number (let it be named SN) which is obtained from the divisor (which is explained below). Then the dividend is shrinked by using this number. The detailed procedure is explained below. SN is obtained by using the formula depending upon the series to which the number belongs. The formulas are as follows: 1. If the number belongs to the series 11, 21, 31, 41, 51, 61………… Then the formula to obtain the SN is (4* number+1)/10

2. If the number belongs to the series 3, 13, 23, 33, 43, 53, 63………….

Then the formula to obtain the SN is (3*number+1)/10

3. If the number belongs to the series 7, 17, 27, 37, 47, 57…………. Then the formula to obtain the SN is (2*number+1)/10

4. If the number belongs to the series 9, 19, 29, 39, 49, 59…………. Then the formula to obtain the SN is (1*number+1)/10

Note: If the divisor is from 1st or 3rd series then the dividend must be even as the SN is of the form a/2. So if the dividend is odd add the divisor to the dividend to make it even. Examples 1. Suppose the divisor is 23 and dividend is 12328 Step1: So SN is (3*23+1)/10 =7 Step 2: 12328  1232+8*7 = 1232+56 = 1288 1288  128 +8*7 = 128 +56 = 184 184

 18

+4*7 = 18

+28 = 46

Step 3: We can see that 46 is divisible by 23 so the dividend 12328 will be divisible by 23.

2. Suppose the divisor is 7 and dividend is 3941 Step 1: So SN is (2*7 + 1)/10 = 3/2 Step 2: Since divisor is odd first add 7 to it 3941 + 7 = 3948 3948  394 + 8 *3/2 = 394 + 12 = 406 406  40 + 6 *3/2 = 40 + 9 = 49 Add 7 to 49 as it is odd so 49 + 7 =56 56  5 + 6 *3 /2 = 5 + 9 = 14 14  1 + 4 *3/2 = 1 + 6 =7 Step 3: We can see that 7 is divisible by 7 so the dividend 3941 is divisible by 7.

Note: We can move from step2 to step3, the result will be same. More to do using this method

1. To find the quotient and the remainder using this method 2. To use the same thing to check whether a number is prime or not