Gouman wrote:I tried searching but, I found no answers that satisfied me.
Can anybody offer any tips for breaking up larger numbers into primes
for example a problem in the Manhattan guides for the prime factorization of
84,700. I just got stuck by the size of the number.
Usually I will just start halving until the numbers become more manageable, but, when dealing with a beast like 84,700 I'm freezing up.
first split the number 847 and 100
the problem here is to factorize 847 because it doe not have 2,3 or 5 as factors.
here is a tip you can use to find whether a number is multiple of 7,11,13 or any other number.
let's say that you want to find whether 847 is multiple of 7
try to find a number x, such 847 - 7x ends in 0
for example 1 ---> 847 - 7(1) = 840. now drop the 0
is 84 multiple of 7? you may not know this but repeat the process
try to find a number x, such 84 - 7x ends in 0
x = 2 ---> 84 - 7(2) = 84 - 14 = 70. now drop the 0
is 7 a multiple of 7? yes so 847 is a multiple of 7.
let's say now that you want to factorize 377
it's clear that 2,3 o 5 are not among its factors.
let's try 7
377 - 7*11 = 300 drop the 0's --> is 3 a multiple of 7? no
try 11
377 - 11*7 = 300 drop the 0's ---> is 3 a multiple of 11? no
try 13
377 - 13*9 = 260 drop the 0 ---> is 26 a multiple of 13? yes so 13 is a factor of 377
a trick to find whether a number is multiple of 11 is the following
let's say that you have a three digit number x = ABC and you want to find out whether x is multiple of 11 or not.
sum and rest its digits in this way
A - B + C
if the result is 0 or a multiple of 11 the number is multiple of eleven
if you have a 4 digit number ABCD
A - B + C - D
for instance
847 --> 8 -4 + 7 = 11 so 847 is multiple of 11
if you are interested in this kind of tricks, I recommend you read "secrets of mental math".
