What is the greatest perfect square that is a factor of the number 650 and how to solve it?
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how to do math the answer is 4/18^32
To find the greatest perfect square that is a factor of a given number, you need to prime factorize the number and find the highest power of each prime factor. Then, you can take the product of these highest powers to obtain the greatest perfect square.
Let's solve it step by step for the number 650:
1. Prime factorize the number 650:
Start by dividing the number by the smallest prime, which is 2.
650 ÷ 2 = 325
325 is not divisible by 2, so try the next prime, which is 3.
325 ÷ 3 = 108.333 (not divisible by 3)
Next, try prime number 5.
325 ÷ 5 = 65
65 is divisible by 5, so continue dividing until we can't anymore:
65 ÷ 5 = 13
Therefore, the prime factorization of 650 is 2 × 5 × 5 × 13.
2. Identify the highest power of each prime factor:
In this case, 2 appears to the power of 1, 5 appears to the power of 2, and 13 appears to the power of 1.
3. Take the product of the highest powers of each prime factor:
2^1 × 5^2 × 13^1 = 10 × 25 × 13 = 3250
Therefore, the greatest perfect square that is a factor of 650 is 3250.
650 = 2 * 5^2 * 13
so 25 is the biggest perfect square (5's power is a multiple of 2)
check: 650 = 25*26