Q: If the product of two numbers is an integer then the two numbers must be integer?

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The largest integer that is not the product of two or more different primes would be the largest prime number. Because there are an infinite number of prime numbers, there is no largest integer that is not the product of two or more different primes.

yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.

no eg: 9x4=36

As there are two consecutive integers then one must be an even number and the other an odd number. If the numbers are y and y + 1 then if y is even, y + 1 is odd and if y is odd then y + 1 is even.The product of an even integer and an odd integer is always even.The question therefore has no answer.121 = 112 but this is not what the question has asked.

Complex numbers, Real numbers, Rational numbers, Integers, Natural Numbers, Multiples of an integer.

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It is not possible to have the product of an integer. "product" is a binary operation and that means that it is an operation that combines two numbers to make the product - a third number. So you need two numbers as input, not just one.

The largest integer that is not the product of two or more different primes would be the largest prime number. Because there are an infinite number of prime numbers, there is no largest integer that is not the product of two or more different primes.

because an integer is a whole number. So the product must be a whole number.

It can be, but need not be. [sqrt(5)+sqrt(2)] and [sqrt(5)-sqrt(2)] are both irrational. Their product is 5-2 = 3. The two numbers are conjugates of one another and the property that their product is an integer is used to rationalise denominator of surds.

yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.

None. The sum or product of any two even numbers must be even.

Assuming the numbers are positive, the answer will be a mixed number that is greater than the integer parts of the two numbers and smaller than the product of one more than each of the two integer parts. The last part is: ax < ab/c * xy/z < (a+1)*(x+1)

no eg: 9x4=36

One or both of the numbers must be zero.

The product of two rational numbers is always a rational number.

-- The product is an integer. -- If the original two integers are both positive, then the product is positive. -- If the original two integers have different signs, then the product is negative.

At least one of the two numbers has to be even, but both can be even.