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Q: [2] Among all of the pairs of numbers whose sum is 8, find the pair with the largest product. What is the product?

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35

There are infinitely many such product pairs.

Pick pairs of prime numbers. Pick any pairs of prime numbers.

Squares of prime numbers, among others.

9-9

The pairs that are relatively prime.

Relatively prime numbers are numbers which share no common factors. This means the numbers are both the product of an entirely different set of prime numbers. There is no limit to the number of prime numbers. Thus there is no limit to the number of relatively prime pairs. Therefore there cannot be two "largest" relative primes.

Yes. Factors are numbers that multiply to create a product.

4 and 9 11 and 12

The product of two numbers is the resulting number when they are multiplied together. As there is an infinite amount of numbers it would be impossible to write out the result of the product of all pairs of numbers

The long but fool-proof way is to find the complete prime factorisation of the number. Then group all the factors into pairs, rejecting any that cannot be paired. The product of the numbers that are left is the largest square factor.

It means write down three pairs of numbers that are relatively prime like 4 and 9, 5 and 6, 13 and 25

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