User:Ibraheem foqara

Ibraheem's divisibility theory is a new way for division with only addition and multiplication operations and only one easy division operation. Where the known division ways uses a lot of division operations which take more time for computer to calculate than addition and multiplication. The theory can help us to know if any number divides any prime number except 2,5 which are easy to check for them. For example we can know if the number m=1718364 divide other prime number p=13 with only one division operation , If the prime number p units digit is 1 : We can write it as x1, where x is the whole number without the units digit. We have to multiply m units digit by (9x+1 ),and add it to (m without the units digit) , For example if m=137,and p=11 》 so x=1, m without the units digit = 13, m units digit =7 So :p divides m (11 divides 137) only if 11 divides 7*(9*1+1)+13=83. If p units digit is 3, we have to multiply the units digit of m by 3x+1 and continue with the same way. If p units digit is 7, we have to multiply the units digit of m by 7x+5 and continue with the same way. If p units digit is 9, we have to multiply the units digit of m by x+1 and continue with the same way. We can repeat the same function until we reach small numbers, which we can divide by easily , Examples : 1)Does 31 divide 1767 ? 31 units digit is 1 So we use 9x+1 to multiply by, Where x=3, so we have to multiply by 9x+1=9*3+1=28 》31 divides 1767 only if 31 divides 176+7*28=372 》31 divides 1767 only if 31 divides 37+2*28=93 . 93/31=3 》31 divides 93》 31 divides 1767. 2)Does 43 divide 58222 ? 43 units digit is 3 So we use 3x+1 to multiply by , Where x=4, so we have to multiply by 3x+1=3*4+1=13 》43 divides 58222 only if 43 divides 5822+2*13=5848. 》43 divides 58222 only if 43 divides 584+8*13=688. 》43 divides 58222 only if 43 divides 68+8*13=172 》43 divides 58222 only if 43 divides 17+2*13=43 》43/43=1》 43 divides 43 》 43 divides 58222. 3)Does 7 divide 3073 ? 7 units digit is 7 So we use 7x+5 to multiply by, Where x=0, so we have to multiply by 7x+5=7*0+5=5 》7 divides 3073 only if 7 divides 307+3*5=322 . 》7 divides 3073 only if 7 divides 32+2*5=42 . 》42/7=6》 7 divides 42 》 7 divides 3073 . 4)Does 379 divide 136440 ? 379 units digit is 9 So we have to use x+1 to multiply by , Where x=37, so we have to multiply by x+1=37+1=38 》379 divides 136440 only if 379 divides 13644+0*38=13644. 》379 divides 136440 only if 379 divides 1364+4*38=1516. 》379 divides 136440 only if 379 divides 151+6*38=379. 》379/379=1》 379 divides 379》 379 divides 136440.