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Is 5184 a perfect square?
Yes. 72 x 72 = 5184. You use prime factorization. The prime factorization of 5184 is 2^6 x 3^4 or 2^2 x 2^2 x 2^2 x 3^2 x 3^2 Take the square root = 2 x 2 x 2 x 3 x 3 = 72 Small note: ^ indicates a power.
What are two prime numbers whose sum is 42?
Split the number in half and make an equation adding the two together to make the desired amount. Unless the number that is half the total is prime, adjust the first number down by an amount to make it a prime number, then adjust the second one up by an equal amount and check whether it is also a prime number. If the second number is also a prime number, you have found two prime numbers that equal the desired amount. If not, adjust the first number down to another prime number, repeating the procedure above until you have two prime numbers.If you split 42 in half, the result is 21. Take the equation 21 + 21 = 42. Since 21 is not prime, adjust the first number down to 19 which is the first prime number below 21. That means the other number would be 23, which is prime. So, you have two prime numbers that add up to 42 = 19 + 23.The prime factorization of 42 is 2 x 3 x 7, so it has three factors that are prime: 2, 3, and 7.
Common multiples of 2 8 12?
To find a common multiple of 2, 8, and 12, we need to look at their prime factorization (the stuff you multiply together to get those numbers). 2 is prime. 8 = 2*2*2. 12 = 2*2*3. So, if we want to have a number that is a common multiple of 2, 8, and 12, it must be composed of the greatest amount of each prime number that 2, 8, and 12 have. So, it must be at least 2*2*2 * 3 = 24. So any common multiple will be of the form 24 * k, where k is any integer. So for example: k=1, 2, 3, 4, ... 24, 48, 72, 96, etc...
Find the smallest integer k such that 756k is a perfect cube?
Factor 756 into prime factors. Then add additional prime factors, such that each prime factor occurs a number of times that is a multiple of 3. The product of the additional prime factors is "k".
Is 81 prime?
81 is not prime: It is 3 x 3 x 3 x 3 (34) or 9 x 9 (92).
