Seventy students occupy a large lecture hall at a large university. Unfortunately, there are 70 students enrolled in this class and only 70 chairs for them to sit in. So, there are just enough chairs for the entire class. There are several different ways that the chairs could be arranged in rows. Using the factors of 70, find the ways that the chairs could be arranged in the classroom.

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70

The factors for 70 can be found by looking at all of the numbers that are 70 and fewer. Ask yourself. Does that number divide into 70 without a remainder? If so, then that number is a factor for 70. If not, then it isn’t a factor for 70.

So, the factors for 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

With the classroom of seventy students. The chairs may be arranged according to each factor. There could be one long row of 70 chairs or 70 rows of 1 chair. Neither of those would be a good idea. Those probably wouldn’t work. Two rows of 35 or 35 rows of 2 probably wouldn’t work either. Those rows would be too long. So, the rest of the factors could be possible. There could be 5 rows of 14 or 14 rows of 5 chairs. There could be 7 rows of 10 chairs or 10 rows of 7 chairs.

Challenging Questions

At the Parkerville Zoo, there is a total of 70 different kinds of animals. A field trip has been planned for the kindergartners from a local school. The teacher wants the students to analyze each kind of animal for a certain period of time. She groups each area of the zoo with the same number of kinds of animals. Each group has 7 kinds of animals in each group.
How many groups are there?
Use the factors of 70 to answer the question.

Answer

There would be 10 groups of animals. This is because there are 7 kinds of animals in each group. Ten’s factor partner is 7 because 7 times 10 equals 70.

At a local library, there is a system in place in order to ensure that people are not spending too much time on the computer. So, the library requires that each person who wants to use the internet for their personal use must sign in a log book. It also lets the library know if someone was getting on an inappropriate site. There are 70 entries in a log book showing entries of those who used the computer at the library during the day. There is an average of 14 people per hour.
How many hours did people use the computers at the library?
Use the factors of 70 to answer the question.

Answer

If there is an average of 14 people using the computers at the library per hour, then they used the computers for 5 hours because 5 times 14 equals 70.

A metal detection club is carefully analyzing 70 square feet of beach for treasures using their metal detectors. There are 14 people in the club. They divide the area equally among the 14 people.
How much space will each person be responsible for given the amount of 70 square feet?
Remember to use the factors of 70 to find your answer.

Answer

There would be 5 square feet of analysis for each person. Fourteen’s factor partner is 5 because 5 times 14 equals 70.

Frequently Asked Questions

There is a difference between divisibility rules and factoring. Factoring like with 70 has to do with finding the numbers that equally divide into a number without having a remainder. These would be 1, 2, 5, 6, 10, 14, 35, and 70. Divisibility rules are the rules that are associated with how to divide certain numbers. In this case, the rules of divisibility will apply to factoring. You will use these divisibility rules to find the factors. Factoring can also have to do with another math skill.

If a number ends in 5 or 0, that number is evenly divisible by 5. So, the number 35, 45, 55, 60, 70 and 80 are just a few of the numbers that can be divided by 5 without having a remainder. This will influence someone finding the factors of that number because you would be trying to find those numbers that can be divided by a number without having a remainder. This would make it easy since you would automatically know that 5 would be a factor of this number like 70. You would then have to find its factor partner. For 70, 5’s factor partner is 14 because 5 times 14 is 70.

To find the factors of 70, first write down 1 and the number itself. Then see if it is an even number. Since 70 is, then 2 and its factor partner, 35 would be factors. Let’s see if 3 will evenly divide into 70 without having a remainder. There would be a remainder, so 3 is not a factor of 70. Then, see if 4 can divide into 70 without a remainder. It doesn’t either. The next step is to try each number after that. In this case, there are only a few more numbers that would be factors for 70.