What numbers have only 3 as a prime factor? Greatest common factors are most often used when reducing fractions. More interesting are properties of classes of numbers, and how many factors they have. First, you would list the factors of each number, the numerator and the denominator, like this: Sign up for free to access more Math resources like.
Now, look only at the underlined numbers.
Some numbers have more than two factors, like A number is divisible by 3 only if the sum of its digits is. This is standard notation, but not absolutely necessary.
Second, if a number is a perfect square, it has an odd number of factors. How about three factors? Last, you would look at all the underlined numbers, and find the greatest number, which in our example is All the numbers above 2 that are the squares of odd primes have exactly 3 factors: We can generalize this and state the rule in a couple of different ways.
As it turns out, the only positive integers with exactly three factors are the squares of primes. Now, underline the factors that these two numbers have in common, like this: The factors of 16 are 1, 2, 4, 8, and 16, some of which pair off: Then, you would underline the common factors, like this: This tells you that you can reduce the fraction by 6, like this: The greatest common factor between 75 and is Greatest Common Factor After you learn how to find factors, you may be asked to find the greatest common factor GCF between two numbers.
We can see that the greatest number we have on our common factors list is 8, so 8 is our greatest common factor.
Wyzant Resources features blogs, videos, lessons, and more about Math and over other subjects.What are the properties of numbers that have as factors one, itself, and one other number? As it turns out, the only positive integers with exactly three factors are the squares of primes.
For instance, the factors of 9 are 1, 3, and 9, and the factors of 49 are 1, 7, and All Factors of a Number. Go straight to Factors Calculator. Factors are the numbers you multiply together to get another number: Actually the calculator first works out the prime factors, then combines them together to discover all other numbers that can be multiplied to achieve your number.
All numbers have 2 factors in that they can all evenly divide by 1 and themselves.
If a number has only 2 factors, then it is prime. The first 3 prime numbers are 2, 3 and 5. Here's a list of composite numbers up to You can see that they can all be factored further.
For example, 4 equals 2 times 2, 6 equals 3 times 2, 8 equals 4 times 2, and so forth. Numbers less than that have exactly three factors are four, nine, 25 and All of these numbers are squares of prime numbers, which means that their only factors are one, themselves and their square roots.
Two squared is four, three squared is nine, five squared is 25 and seven squared is Some numbers have more than two factors, like Factors of 10 would include, of course, 1 and 10, but they would also include 2 and 5, because 2 x 5 = Therefore, if we were asked to list factors of 10, we would write: 1, 2, 5,Download