I want to make sure I'm doing the GCF correctly with 3 numbers. The problem is: Ari is making patriotic pins. He has 105 red ribbons, 147 white ribbons, and 189 blue ribbons. What is the greatest number of identical pins he can make if he uses all his ribbons? I think the answer is 21. Is that correct? Thanks..
21 is correct.
When in doubt, do one of the following:
1. Find GCF for two numbers at a time, the first time using two original numbers. The second time use the first GCF and the third number.
2. Divide each original number by the GCF found. If the numbers don't divide, there is a mistake. If there is a GCF between the three GCFs, then some factors were missing from the original GCF.
To find the greatest common factor (GCF) of three numbers, such as 105, 147, and 189, you can follow these steps:
1. Make a list of the common factors of the three numbers. These are the numbers that divide evenly into all three numbers.
For 105: The factors are 1, 3, 5, 7, 15, 21, 35, and 105.
For 147: The factors are 1, 3, 7, 21, 49, and 147.
For 189: The factors are 1, 3, 7, 9, 21, 27, 63, and 189.
2. Identify the greatest number that appears in all three lists. This number is the GCF.
From the lists above, we can see that the greatest common factor of 105, 147, and 189 is 21, just as you mentioned.
Now, let's verify if 21 is indeed the correct answer to the problem you provided.
If Ari wants to make identical pins, he needs to have an equal number of each color ribbon. Since the GCF is 21, it means he can make 21 identical pins using 21 red ribbons, 21 white ribbons, and 21 blue ribbons. This distribution ensures that all the ribbons are used up and that each pin has the same number of ribbons.
So, your answer of 21 is correct. Ari can make 21 identical pins using all his ribbons. Well done!