CramX Logo

Q
QuestionMathematics

What is the greatest perfect square that is a factor of 90?
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

Step 1:
I'll solve this step by step using the specified LaTeX formatting guidelines:

Step 2:
: Find the prime factorization of 90

90 = 2 \times 3^{2} \times 5

Step 3:
: Identify the possible perfect square factors

- $$5^{0}
To create a perfect square, we need to use even powers of prime factors. From the prime factorization, we can use:

Step 4:
: Construct the largest perfect square factor

2^{0} \times 3^{2} \times 5^{0} = 1 \times 9 \times 1 = 9
The largest perfect square will use the maximum even powers:

Step 5:
: Verify the result

- 9 is a perfect square ($$3^{2}$$)
- 9 is a factor of 90 (90 \div 9 = 10) - No larger perfect square exists as a factor of 90

Final Answer

9