Greatest Common Factor Calculator
We will learn the relationship between H.C.F. and L.C.M. of two numbers. Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is Highest common factor and lowest common multiple of two numbers are 18 and respectively. Learn how to find the greatest common factor using factoring, prime factorization and the Euclidean For example, for the set of numbers 18, 30 and 42 the GCF = 6. The factors of are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, Learn how to find the GCF (greatest common factor) of two monomials or more.
Given the list of common factors for each number, the GCF is the largest number common to each list. Find the GCF of 18 and 27 The factors of 18 are 1, 2, 3, 6, 9, The factors of 27 are 1, 3, 9, The common factors of 18 and 27 are 1, 3 and 9. The greatest common factor of 18 and 27 is 9.
Greatest common factor of monomials (article) | Khan Academy
Find the GCF of 20, 50 and The factors of 20 are 1, 2, 4, 5, 10, The factors of 50 are 1, 2, 5, 10, 25, The factors of are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, The common factors of 20, 50 and are 1, 2, 5 and Include only the factors common to all three numbers. The greatest common factor of 20, 50 and is Prime Factorization To find the GCF by prime factorization, list out all of the prime factors of each number or find them with a Prime Factors Calculator.
List the prime factors that are common to each of the original numbers. Include the highest number of occurrences of each prime factor that is common to each original number. Multiply these together to get the GCF. You will see that as numbers get larger the prime factorization method may be easier than straight factoring. The occurrences of common prime factors of 18 and 27 are 3 and 3. Even though the two classes have to take a different number of exams, their teachers have told them that both classes-- let me underline-- both classes will get the same total number of exam questions each year.
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What is the minimum number of exam questions William's or Luis's class can expect to get in a given year? So let's think about what's happening. So if we think about Luis's teacher who gives 30 questions per test, so after the first test, he would have done 30 questions.
GCF & LCM word problems
So this is 0 right over here. Then after the second test, he would have done Then after the third test, he would have done And after the fourth test, he would have done And after the fifth test, if there is a fifth test, he would do-- so this is if they have that many tests-- he would get to total questions. And we could keep going on and on looking at all the multiples of So this is probably a hint of what we're thinking about.
We're looking at multiples of the numbers. We want the minimum multiples or the least multiple.
Multiples and Factors
So that's with Luis. Well what's going on with William? Will William's teacher, after the first test, they're going to get to 24 questions. Then they're going to get to 48 after the second test.
Then they're going to get to 72 after the third test. Then they're going to get to I'm just taking multiples of They're going to get to 96 after the fourth test. And then after the fifth test, they're going to get to And if there's a sixth test, then they would get to And we could keep going on and on in there.
But let's see what they're asking us. What is the minimum number of exam questions William's or Luis's class can expect to get in a year? Well the minimum number is the point at which they've gotten the same number of exam questions, despite the fact that the tests had a different number of items. And you see the point at which they have the same number is at This happens at They both could have exactly questions even though Luis's teacher is giving 30 at a time and even though William's teacher is giving 24 at a time.
And so the answer is And notice, they had a different number of exams. Luis had one, two, three, four exams while William would have to have one, two, three, four, five exams. But that gets them both to total questions. Now thinking of it in terms of some of the math notation or the least common multiple notation we've seen before, this is really asking us what is the least common multiple of 30 and And that least common multiple is equal to Now there's other ways that you can find the least common multiple other than just looking at the multiples like this.
You could look at it through prime factorization.
Relationship between H.C.F. and L.C.M.
So we could say that 30 is equal to 2 times 3 times 5. And that's a different color than that blue-- 24 is equal to 2 times So 24 is equal to 2 times 2 times 2 times 3.
So another way to come up with the least common multiple, if we didn't even do this exercise up here, says, look, the number has to be divisible by both 30 and If it's going to be divisible by 30, it's going to have to have 2 times 3 times 5 in its prime factorization.
That is essentially So this makes it divisible by And say, well in order to be divisible by 24, its prime factorization is going to need 3 twos and a 3. Well we already have 1 three.
And we already have 1 two, so we just need 2 more twos. So 2 times 2.Finding the Greatest Common Factor
So this makes it-- let me scroll up a little bit-- this right over here makes it divisible by And so this is essentially the prime factorization of the least common multiple of 30 and