Number of perfect square factors of number 4500?

Question

Answer

Number of Perfect Square Factors of 4500

The first step is to find the prime factorization of 4500. This can be done by dividing 4500 by prime numbers starting from 2.

Prime Factorization of 4500

Therefore, the prime factorization of 4500 is 2^2 * 3 * 5^3.

Finding Perfect Square Factors

Perfect square factors are obtained by selecting a combination of the prime factors in pairs and raising them to even powers.

For 2^2, the possible combinations are 2^0, 2^2. So, we have 2 perfect square factors for 2^2.

For 3, the possible combinations are 3^0. So, we have 1 perfect square factor for 3.

For 5^3, the possible combinations are 5^0, 5^2. So, we have 2 perfect square factors for 5^3.

Total Perfect Square Factors

By multiplying the number of perfect square factors for each prime factor, we get the total number of perfect square factors of 4500.

2 perfect square factors for 2^2 * 1 perfect square factor for 3 * 2 perfect square factors for 5^3 = 2 * 1 * 2 = 4

Conclusion

Therefore, the number of perfect square factors of 4500 is 4.