There are a few ways to go about factoring. You can decide what works best for you. I always find the prime factorization first. Let's look at a random number: 108
The prime factorization can be found by using a factor tree.
108
54,2
27,2,2
9,3,2,2
3,3,3,2,2
2^2 x 3^3 = 108
Half of the factors will be less than the square root, half greater. If the number is a perfect square, there will be an equal number of factors on either side of the square root. In this case, the square root is between 10 and 11.
Adding one to the exponents of the prime factorization and multiplying them will tell you how many factors there are. In this case, the exponents are 2 and 3. Add one to each. 3 x 4 = 12
108 has 12 factors. Six of them are 10 or less, six of them are 11 or greater. All we have to do is divide the numbers one through ten into 108. If the result (quotient) turns out to be an integer, you've found a factor pair. Knowing the rules of divisibility will make that even easier.
108 is divisible by...
1 because everything is.
2 because it's even.
3 because its digits add up to a multiple of 3.
4 because its last two digits are a multiple of 4.
6 because it's a multiple of 2 and 3.
9 because its digits add up to a multiple of 9.
That's six factors less than 10. Divide them into 108. That's the rest of them.
(108,1)(54,2)(36,3)(27,4)(18,6)(12,9)
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Notice that all of those numbers, except for 1, can also be found in the prime factorization.
This is a tricky prospect because you have to systematically go through all its prime factors to find all factors.
But I like this way of double-checking whether I have them all:
Suppose the number is n.
And suppose pk represents the kth Prime number.
Now, if the prime factorization of n = p1a1 x p2a2 x p3a3 *... pkak
Then the number of factors n has is (a1 + 1) x (a2 + 2) x ... x (ak + 1)
Then you just have to systematically go through the prime factors, multiplying all combinations of them together, to get all the factors, but don't forget 1 and the number itself.
Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.
This number would have to be a squared number as it only has 15 factors. The number I have calculated is 324 as the square root is 18
The smallest prime factors are 2,3,5,7 thus the smallest number would be the product of these will be 210
I would call an odd number factor a factor that is an odd number. I would call a number with an odd number of factors a perfect square.
I guess it would be 45,63,75,99 they each have 6 factors
How to look up a drivers license number depends upon the state. The best advice would be to contact the state DMV for advice or look on their website and they will give guidance.
if a number has an odd number of factors it would be a perfect square
if a number has an odd number of factors it would be a perfect square
to get the factors of a number you figure out what numbers multiplied together would equal the number youre trying to get factors for
The factors for the number 38 would be 1,2 and 19. This is a math problem.
The advice that I would give for building a deck would be to have someone do it for you and maybe once you see them doing it they can teach you a little bit on the information on what and how they did it.
The factors for the number 30 would be 1,2,3,5,6,10, 15 and 30. This is taught in math.
I would be very cautious when it comes to free financial advice. However, if you have a financial institution with whom you have a loan, bank account or other financial dealings, I would go to them for advice. They are someone who would have something to loose if they have out poor financial advice.
You could find advice for someone with no work experience through friends and family members. To make sure you get the best possible advice, you would need to ask someone with experience.
Some people would call that the proper factors. Others maintain that proper factors do not include the number 1.
Because someone asked me to.
no, factors of a number would be less than that of the original number. A prime number is a number that has factors of only itself and 1.