Prime Numbers, Prime Factors and Composite Numbers 5 - Reasoning

Esin attempted to determine the prime factors of the number 84 using a factor tree, which is a method of breaking down a composite number into its prime components. However, she made a mistake in her process. She started correctly by dividing 84 into 3 and 28. But then, instead of breaking down 28 into its prime factors, she listed 9 and 3, which is incorrect because 9 is not a prime number. Consequently, she incorrectly identified 3, 9, and 28 as the divisors of 84.

To correct her mistake, the factor tree should show that 28 can be further divided into 4 and 7. Since 4 is not a prime number, it should be broken down further into 2 and 2, which are prime. Therefore, the correct prime factors of 84 are actually 2, 3, and 7. The factor tree should illustrate that 84 is divided into 3 and 28, then 28 into 4 and 7, and finally, 4 into 2 and 2. This correction reveals that the prime divisors of 84 are not 3, 9, and 28, but rather 2, 3, and 7, with 2 appearing twice in the factorisation.