Q: CAn you prime factor 46692 in your head? Need it FOr my math homework?
A: i'm stopping if i have to check past 127. that's my new rule. 46692, even, so halve it, 23346, and again, a little more difficult, my trick is digit by digit but for odd digits go one lower and then add 5s back, one digit to the right of where the odd digits were. so 11123, then put the 5s back as 11673. checking for 3, it's just adding up the digits, and you can knock them out as you see them. 1167 digits add up to 15, so yes, we have 3 in it. must divide 11673 by 3. knock off the 3, is 1167, add 3 is 117(0), 117 is 9 times 13 or 39 times 3. so retrace the steps, 39 times 3 is 117, need to go down to 1167 (from 1170) which means 390 minus 1, is 389, then the other way to add 3 (for 11673) means add 1 to 389 in the next digit, so 3891. so 3x3891 should be 11673, does that look right. yes. Check for 3 again, in 3891, it's there again, because knock the 9 and knock the 8 and 1, and 3 left. how about 3000 and 810 and 81. so 1000 plus 270 plus 27. 1270 plus 27. 1297. so 1297x3=3891, does that look right. yes it does. Ok so check for 7, knock it off the right leaves 129, known to be 43, so 7 is out. checking 11 (in 1297), knock it off the left, 197, already no because it would need to be 198, so no 11. checking 13, well 3 more is 1300 so no. checking 17 (in 1297), take it off the right, it's 128, that's a power of 2 so no way. checking 19, 1297 minus 57 is 124, in half is 62, then 31, so no. Being aware of the limits here, we only have to check up to the square root of the target number, so right now that means the square root of 1297. 30 squared is 900, and 40 squared is 1600, so certainly 37 is already too high to check, so this shouldn't take long even at worst. which it likely is, because the chances get less and less of finding a match as you move up. so next to check is 23, checking in 1297, add it, is 1320, 132, in half is 66, that's just 11, so no. 29, trick for that is 203, added to 1297 is 1500, so no. 31, tripled is 93, 1297 plus 93 is 139(0), plus 31 levels it off at less than 200 so that means a result less than 20, so not 31. 37 has virtually no chance of being it because i think its square is too high, and if we're correct so far, the only option left anyway would have to be a square, which would have to end in 9, but i'll check anyway in case i've made a mistake, 1297 minus 37 is 126(0), in half is 63 (known 9x7) so no. so retracing our steps the final answer would 2x2x3x3x1297