Thread: factors

how do you find out all the factors of a number in 10 seconds?? i take ages to find out all of the factors - there has to be an easier way!! please help me

Originally Posted by kate

how do you find out all the factors of a number in 10 seconds?? i take ages to find out all of the factors - there has to be an easier way!! please help me

Hi

I don't understand the question. Can you explain what you have so far?

Thanks

Hi:
Ex 1: List all factors of 1248.

Solution:
Check 1 (trivial): Trivial factors are 1 and 1248.
Check 2: 1248/2=624. Thus two factors are 2 and 624.
Check 3: 1248/3=416 " " " " 3 and 416
Check 4: 1248/4=312 " " " " 4 and 312
Check 5: no
Check 6: 1248/6=208 " " " " 6 and 208
Check 7: no
Check 8: 1248/8=156 " " " " 8 and 156
Check 9: no
Check 11: no
Check 12: 1248/12=104 " " " " 12 and 104
etc.

Factors of 1248:{1, 1248, 2, 624, 3, 416, 4,3 12, 6,
208, 8, 156, 12, 104, 13, 96, 16, 78, 24, 52, 26, 48, 32, 39}.

Hint: You can stop your search at sqrt(n). In the present case, sqrt(1248)=35.327... Therefore check natural numbers to 35.

Method2 (easy):


Use mod key on calculator.


Ex 2: List factors of 330.


Solution:

Enter 330 into memory (330 STO).


Sqrt(330) = 18.17... Therefore check up to 18.


On calculator, systematically enter (MR)mod(k) for all k in {1, 2, 3, ..., 18} (MR <=> MEM-RECALL). You can isolate factors by utilizing the fact that k is a factor of n iff n_mod(k)=0. For example, 330mod(8) = 2. Thus 8 is not a factor of 330. 330mod(15)=0. Thus 15 is a factor, as is 22 (330/15=22).


Regards,


Rich B.