Video: Solving Word Problems Involving the Highest Common Factor

Scarlett baked 10 chocolate muffins and 15 blueberry muffins. She wants to divide them into boxes to give to her friends. Each box must contain only 1 type of muffin, and there must be the same number of muffins in each box. What is the largest number of muffins that she can put in each box? How many boxes will she need?

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Video Transcript

Scarlett baked 10 chocolate muffins and 15 blueberry muffins. She wants to divide them into boxes to give to her friends. Each box must contain only one type of muffin, and there must be the same number of muffins in each box. What is the largest number of muffins that she can put in each box? How many boxes will she need?

We are told that Scarlett baked 10 chocolate muffins and 15 blueberry ones. As she wants to put the same number of muffins in each box. We need to work out the highest common factor of 10 and 15. This is the highest number that divides exactly into 10 and 15.

The factors of 10 are one, two, five, and 10. This is because one multiplied by 10 is equal to 10, and two multiplied by five is equal to 10. The factors of 15 are one, three, five, and 15. One multiplied by 15 is 15, and three multiplied by five is 15. There are two common factors, one and five. Therefore, the highest common factor of 10 and 15 is five.

As Scarlett baked 10 chocolate muffins, these can be put in two boxes of five. There were 15 blueberry muffins, and these can be boxed in three boxes of five. Two plus three is equal to five. Therefore, there will be five muffins in five boxes. The largest number of muffins that Scarlett can put in each box is five. And she will need five of these boxes.

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