A football team’s record is 75 wins and 25 losses. Express these numbers as products of their prime factors.
Writing a number as the product of its prime factors is also known as prime factorization. We know that any prime number has exactly two factors, one and itself. The only even prime number is two. The next five prime numbers after this are three, five, seven, 11, and 13. All of these numbers are only divisible by one and the number itself.
In order to write the numbers 75 and 25 as products of their prime factors, we can use a factor tree. Let’s begin with 25. The only prime number that divides exactly into 25 is five. This is because it is a square number; five multiplied by five or five squared is 25. Our factor tree is completed. And 25 is equal to five squared.
The smallest prime number that divides into 75 is three. As three multiplied by 25 is 75, these are our two branches. Three is prime, so we can circle this. And this path is finished. As we have already seen, 25 is equal to five multiplied by five. As both of these are prime, our factor tree once again is complete. 75 written as a product of its prime factors is three multiplied by five squared.
Whenever possible, we wrote these answers in exponent form. The answer for 75 could also be written as five squared multiplied by three. And the multiplication sign could be replaced by a dot.