A truck is traveling down the highway at 40 miles an hour. The driver slows the truck down by pressing the brake pedal every few times. If the speed of his truck evenly drops with each press of the brake pedal, how many times will the truck driver need to press the brake pedal in order to stop the vehicle.
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Use factors of 40 to determine how to explain this problem. In other words, there will be multiple answers to this question. Once you figure out the possibilities, see if you can describe them.
Factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40
The factors for 40 can be found by looking at all of the numbers that are 40 and fewer. Ask yourself. Does that number divide into 40 without a remainder? If so, then that number is a factor for 40. If not, then it isn’t a factor for 40.
So, the factors for 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
With the truck driver, we need to first find out the factors of 40. These factors include 1, 2, 4, 5, 8, 10, 20, and 40. This means that the truck driver could push the pedal down 8 different amounts because there are 8 factors for 40.
Most likely, the truck driver did not press the brake pedal the lowest factors and the highest factors. The lowest factors like 1 and 2 would mean that the truck driver probably had to mash the pedal quickly.
If he pressed the gas pedal 10, 20 or 40 times, the truck would be lurching forward many times. That probably didn’t happen. Instead, the driver probably pressed the pedal 4, 5, or 8 times.
Challenging Questions
Question 1List the factors of 40
Which positive whole numbers divide 40 without leaving a remainder?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
Each listed number divides the original number evenly.
Question 2Find the factor pairs of 40
Which multiplication pairs have a product of 40?
40 has these positive factor pairs: 1 × 40; 2 × 20; 4 × 10; 5 × 8.
Multiplying the two numbers in any pair gives the original number.
Question 3Prime-factorize 40
What is the prime factorization of 40?
40 = 2 × 2 × 2 × 5.
Every number in the product is prime.
