Introduction
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.
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Challenging Questions
Question 1List the factors of 70
Which positive whole numbers divide 70 without leaving a remainder?
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 70
Which multiplication pairs have a product of 70?
70 has these positive factor pairs: 1 × 70; 2 × 35; 5 × 14; 7 × 10.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 70
What is the prime factorization of 70?
70 = 2 × 5 × 7.
Every number in the product is prime.
