Greatest Common Factor of 18 and 24 GCF(18,24)
We will learn the relationship between H.C.F. and L.C.M. of two numbers. First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3. GCF of 18 and 24, find the biggest number that can divide two integers, calculate factors and the greatest common factor of 18 and LISTING METHOD: 18 = 18, 36, 54, 72, 90, , , , , 24 = 24, 48, 72, 96, , , , , , LCM: GCF: 6.
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.
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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. 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. 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 You take any one of these numbers away, you are no longer going to be divisible by one of these two numbers.
If you take a two away, you're not going to be divisible by 24 anymore. If you take a two or a three away. If you take a three or a five away, you're not going to be divisible by 30 anymore.
And so if you were to multiply all these out, this is 2 times 2 times 2 is 8 times 3 is 24 times 5 is Now let's do one more of these. Umama just bought one package of 21 binders. Let me write that number down. She also bought a package of 30 pencils. She wants to use all of the binders and pencils to create identical sets of office supplies for her classmates. What is the greatest number of identical sets Umama can make using all the supplies? So the fact that we're talking about greatest is clue that it's probably going to be dealing with greatest common divisors.
And it's also dealing with dividing these things.
Relationship between H.C.F. and L.C.M. | Highest common Factor | Solved Examples
We want to divide these both into the greatest number of identical sets. So there's a couple of ways we could think about it.
- GCF & LCM word problems
- Relationship between H.C.F. and L.C.M.
- What is the gcf of 18 and 24?
Let's think about what the greatest common divisor of both these numbers are. Or I could even say the greatest common factor. The greatest common divisor of 21 and So what's the largest number that divides into both of them? So we could go with the prime factor. We could list all of their normal factors and see what is the greatest common one.
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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. The occurrences of common prime factors of 20, 50 and are 2 and 5. Euclid's Algorithm What do you do if you want to find the GCF of more than two very large numbers such asand ? But if you need to do the factorization by hand it will be a lot of work.
Repeat the process subtracting the smaller number from the result until the result is smaller than the original small number. Use the original small number as the new larger number. Subtract the result from Step 2 from the new larger number. Repeat the process for every new larger number and smaller number until you reach zero. When you reach zero, go back one calculation: For additional information see our Euclid's Algorithm Calculator.
Now let's find the GCF of our third value, 20, and our result, Therefore, the greatest common factor of50 and 20 is