Introduction
A package delivery driver sees that he has 14 packages left to deliver. He wants to group them into the northern, southern, eastern, and western areas of town. Then he would drive to each area and deliver each group.
In this case, do you think he could have an equal number of packages in each group, or will there have to be different amounts of packages in each group?
The answer is no. The driver will not have an equal number in each group for each area of town. There are 4 areas of town.
Since there are 14 packages left to deliver, there may be some groups that are the same, but it couldn’t be all 4 groups. Fourteen can’t be divided equally by 4 because there would be a remainder.
Look at the groups of packages below.
The closest would be that there are three groups with four packages in each of those three groups. The last group would only have 2 packages in that group.
There are many other combinations for dividing the 14 packages into 4 groups, but it could never be with an equal number of packages in each group.
Fun Factoring with Fourteen
Why can’t the delivery driver have equal groups of packages? That all has to do with the factors of 14. To have equal groups of something means the number that represents the total amount must have a factor that is the same as the number of groups.
In this case, that is not true. Let’s find out the factors for fourteen. To find out, we will see which numbers 14 or fewer can equally divide into 14. There could be no remainder, or it will not be considered a factor of 14. Let’s gather the factors!
There are not a lot of factors for 14. Actually, there are four factors. One times 14 equals 14, and 2 times 7 equals 14.
Factors of 14 are 1, 2, ,7 and 14
Challenging Problems
Question 1List the factors of 14
Which positive whole numbers divide 14 without leaving a remainder?
The factors of 14 are 1, 2, 7, 14.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 14
Which multiplication pairs have a product of 14?
14 has these positive factor pairs: 1 × 14; 2 × 7.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 14
What is the prime factorization of 14?
14 = 2 × 7.
Every number in the product is prime.
