Factorization method of 3150 to make it a perfect square
You cannot make 3150 a perfect square.
However, since 3150 = 2 * 3^2 * 5^2 * 7, if you multiply it by 2*7 you get
2^2 * 3^2 * 5^2 * 7^2 = (2*3*5*7)^2
To factorize 3150 and make it a perfect square, we need to break it down into its prime factors. Once we have the prime factors, we can determine how to rearrange them to form a perfect square.
Here's how you can factorize 3150 into its prime factors:
1. Start by dividing 3150 by the smallest prime number, which is 2. 3150 ÷ 2 = 1575.
2. Since 1575 is an odd number, it is not divisible by 2. So, we move on to the next prime number, which is 3. 1575 ÷ 3 = 525.
3. Again, 525 is not divisible by 3, so we proceed to the next prime number, which is 5. 525 ÷ 5 = 105.
4. Now, we divide 105 by 5 again. 105 ÷ 5 = 21.
5. Since 21 is an odd number, it is not divisible by 5. We move on to the next prime number, which is 7. 21 ÷ 7 = 3.
6. Finally, we divide 3 by 3, which gives us 1.
Now that we have the prime factors of 3150, we can rearrange them to form a perfect square. We consider each prime factor and check if there is an even power for each prime factor. If there is, we use half of the exponent. Otherwise, we leave it as it is.
The prime factorization of 3150 is: 2 × 3 × 3 × 5 × 5 × 7.
To make it a perfect square, we need to have each prime factor with an even exponent. Looking at the prime factors, we see that the exponent of 2 is 1, and the exponent of 3 is 2. In order to make these exponents even, we can multiply 3150 by 2 and another 3, resulting in 6300.
So, 6300 is a perfect square because its prime factorization is 2 × 3 × 3 × 5 × 5 × 7, with each factor having an even exponent.