Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.

Rewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.

Express composite whole numbers as a product of prime factors with natural number exponents.

A factor is a number that evenly divides another number.

Factors can be thought of in terms of "factor pairs," or numbers that multiply together to make a target number.

Factors of 12: 1, 2, 3, 4, 6, 12

Factor pairs of 12: 1 and 12; 2 and 6; 3 and 4

The result of multiplying a certain number by a whole number

Can also be thought of as “counting by” that number, i.e., counting by 5s will give you a list of multiples of 5

Multiples of 5: 5, 10, 15, 20..... 105, 110, 115....

A list of multiples is infinite.

I want to purchase hot dogs and buns, but the hot dogs come in packs of 6, and the buns come in packs of 8. How many packages of each should I purchase so that I don't have any hot dogs or buns left over?

To solve this problem, we can find the least common multiple of 6 and 8. Start by listing the first few multiples of each.

The least common multiple is 24. That's the smallest number that they both have in common. Now I know that I can purchase 24 hot dogs and 24 buns. My last step is to determine how many packages of each product would give me 24 individual hot dogs or buns.

I need 4 packages of hot dogs, and 3 packages of buns to have no hot dogs or buns left over, and to get the minimum amount of hot dogs and buns possible.

I'm making bookmarks out of ribbon to sell at the school carnival. I have one piece of ribbon that is 24 inches long, and one piece of ribbon that is 20 inches long. If I cut my ribbon into equally-sized lengths, what is the longest length of bookmark that I can make?

In this situation, we need to find the greatest number that will divide both 20 and 24 evenly. This is called the greatest common factor, because it's the largest factor that the two numbers share.

The greatest common factor is 4. That means I can divide both ribbons into 4-inch pieces. How many bookmarks will I make altogether?

Alternatively, I could add up all the ribbon I have at the beginning, and then divide by 4. This will give me the total number of bookmarks, rather than the number of bookmarks I will cut from each piece, as described above.