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.
The positive integer with only one factor is 1.
10 of them.
A prime number is a number with two positive integer factors, while a composite number has more than two positive integer factors. Since the number 0 has no positive integer factors, and the number 1 has just one positive integer factor (itself), neither of these are prime.
The sum of two positive integers is positive
A prime number has two positive integer factors, itself and 1. The number 0 has no positive integer factors, and is therefore not prime. The number 1 has just a single positive integer factor, and once again, is not prime.
Yes it is. One is a factor of every positive integer.
The positive integer with only one factor is 1.
The smallest positive factor of any positive integer is the number 1. If negative factors are allowed, the smallest factor is the negative of the absolute value of any integer.
The greatest factor of any positive integer is itself.
1. It is the lowest factor of any [positive] integer.
1 is the least common factor of any set of positive integers because 1 is a factor of all nonzero integers and 1 is the smallest positive integer.
The lowest factor of any positive integer is 1.
10 of them.
The highest factor of any positive integer is the integer itself. The highest common factor of 91 and 203 is 7.
The largest factor of any positive number is the number itself.
The smallest factor of any positive integer is 1.
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