Question

determine the prime factorization of each of the following; 13915

Answer 1

we see that given number is ending in 5 .  so it is divisble by 5.
13915 / 5 =  2783
it is not even sumber, sum of digits is not divisble by 3, not divisible by 7. Observe that sum of alternate digits (even and odd digits) is same.  So it is divisible by 11.
2783/11 = 253
again the sum off odd digits is same as even digits.
253/11 = 23            we know that 23 is a prime number
So  13915  =  5 * 11 * 11 * 23

Answer 2

AS 13915 IS ENDING BY S0
13915/5=2783
2783 HAS ALTERNATE DIGITS EQUALSO IT IS BY 11
2783/11=253
AS ALTERNATE DIGIGTS ARE AGAIN=SO BY 11
253/11=23
S0 5*11*11*23