Answer:
100 = 2 * 2 * 5 * 5
Explanation:
Step 1: Start by dividing 100 by the smallest prime number:
We need to determine the smallest prime number which 100 can be evenly divided by.
2 is the smallest prime number which evenly divides into 2, so we have:
100 / 2 = 50
2 * 50 = 100
In 2 * 50, 2 is the prime number and we'll use it when trying to write 100 as a product of its prime factors.
Step 2: Divide 50 by the smallest prime number:
The smallest prime number by which 50 can be evenly divided by is also 2:
Thus, we have 50 / 2 = 25
2 * 25 = 50
In 2 * 25, 2 is the prime number and we'll use it when trying to write 100 as a product of its prime factors.
So currently, we have 2 and 2.
Step 3: Divide 25 by the smallest prime number:
The smallest prime number by which 25 can be divided is 5:
Thus, we have 25 / 5 = 5
5 * 5 = 25
Unlike 2 * 50 and 2 * 25, 5 * 5 includes two prime numbers, so we use both numbers when trying to rewrite 100 as a product of its prime factors.
Thus, the four factors we have are 2, 2, 5, and 5.
The numbers are already in order from smallest to largest so we now have:
100 = 2 * 2 * 5 * 5
We can check our work by making sure 2 * 2 * 5 * 5 equals 100:
100 = (2 * 2) * (5 * 5)
100 = 4 * 25
100 = 100
Thus, our answer is correct.