Introduction
Remember back in the olden days when a quarter went so much farther. It seems like today you can’t buy anything for 25 cents anymore. However, as a challenge, we are going to see if we can think of some things that might cost five cents. To use the whole quarter and imagine that there isn’t going to be tax added on, how many items will we need to buy?
First, let’s look at the items. Think about if these items could cost 5 cents if you had the ability to buy them individually. Also, think about how many items you would need to buy to use the whole quarter.
So, could you buy a paper clip, piece of candy, nail, gem, ribbon, sticker, or potato chip for 5 cents each? If so, how many could you buy if they were exactly 5 cents each in order to use up the whole quarter?
Factors of 25 are 1, 5, and 25
To find how many 5-cent items you could buy with your quarter takes the skill of factoring. The factoring of 25 needs to be considered when solving this problem. The factors of 25 are the numbers from 1 through 25 that can evenly be divided into 25 without having a remainder. For this number, there aren’t many of them.
Usually, once you find a number that evenly divides into the original number, there is a factor partner. This means that there is another number that goes with it and is also a factor of this number. In other words, these two numbers multiplied together will equal 25.
Every number has at least two factors, and those are 1 and itself. So, it would be 1 and 25. Since 25 is not an even number, then 2 is not going to evenly divide into 25. We can rule that one out. Next, we will look at 3 and 4. These don’t evenly divide into 25 either.
There would be remainders. Let’s look at 5. Five can evenly divide into 25 without having a remainder. However, what is its factor partner? It must have one. This happens every once in a while. The factor’s partner of 5 is 5 itself because 5 times itself, 5, is 25.
So, unlike other numbers that have an even number of factors, 25 has only 3 factors. These are 1, 5, and 25.
Back to our purchases of 5-cent items, Since each item is worth 5 cents, we would known that 5’s factor partner is also 5 in order to equal 25 when multiplied together.
So, we would need to purchase 5 items at 5 cents each in order to equal 25 cents.
Challenging Questions
Question 1List the factors of 25
Which positive whole numbers divide 25 without leaving a remainder?
The factors of 25 are 1, 5, 25.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 25
Which multiplication pairs have a product of 25?
25 has these positive factor pairs: 1 × 25; 5 × 5.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 25
What is the prime factorization of 25?
25 = 5 × 5.
Every number in the product is prime.
