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 .