Introduction
In a medium-sized city, the tallest building is a downtown skyscraper which houses a large, national bank on the bottom floors. The remainder of the building houses 2 different companies on each of the remaining 78 floors. Each set of floors was grouped according to a certain industry. The industries that are included are education, tourism, retail, hospitality, legal, and advertisement. Using the information about the number of industries, determine the number of floors and number of companies that would be devoted to each industry. Use the factors of 78 to find the answer to the number of floors and the other information provided to find the number of companies that are in each industry.
The Factors Of 78
Number 78 has quite a few factors mainly since it is an even number. However, there are other reasons too. It is a larger number, so many larger numbers have more factors, but that is not always true. A way to find the factors of 78 would be to list all the numbers from 1-78 like the list below. Then you can be assured that all factors will be included.
You need to determine if each number can equally divide into 78 without having a remainder. A calculator may be used. Work the division problem for each possible factor or number between 1 and 78. If there is a remainder, then it is not a factor of 78. All the other numbers that do equally divide into 78 without remainders would be considered factors of it. Remember a factor always has a factor partner. When you multiply the factor number and its partner together, you will get the number, which in this case is 78. Sometimes, a factor’s partner can be itself because the number times itself can equal certain numbers.
The numbers with a remainder should be taken out because they are not factors of 78. You should check each factor by matching it with its factor partner. So, when they are multiplied together, they will equal 78. Below shows the factor number and its partner, which is also a factor of 78.
With the building that has 78 floors besides the ground floor, it is known that there are 6 industries that are allotted to an equal amount of floors in the building. They have been dispersed equally with each floor having 2 companies on it. We need to find 6’s factor partner which is 13. So, this means that each industry has 13 floors for it. Then if each floor has 2 companies on each floor, then there are 26 companies for each industry.
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Challenging Questions
Question 1List the factors of 78
Which positive whole numbers divide 78 without leaving a remainder?
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 78
Which multiplication pairs have a product of 78?
78 has these positive factor pairs: 1 × 78; 2 × 39; 3 × 26; 6 × 13.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 78
What is the prime factorization of 78?
78 = 2 × 3 × 13.
Every number in the product is prime.
