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If all three numbers are positive then the product obviously has to be positive. If TWO of the three numbers are negative, then the product is also positive. But if exactly ONE of the three numbers is negative or if all THREE are negative, then the product must be negative. In general, a product of numbers is negative if an ODD NUMBER of the terms is negative.
No
"Either" is used for two. I'll assume that you mean "larger than ANY of them". The following applies to ANY real numbers.For TWO numbers, the product is larger than either of them if both numbers are greater than one. For THREE numbers, the product is larger than any of them if the two numbers OTHER than the largest number have a product greater than one. For example: 0.5, 3, 5 The largest number here is 5; the product of the OTHER two is 0.5 x 3 = 1.5. Or here is an example with integers: -5, -3, 10 The product of the "other two" numbers is 15, which is larger than one - so the product of all three is larger than the largest number (and therefore, larger than ANY of them). Another example: -5, 1, 10 The product of the two numbers OTHER than the largest is -5 x 1 = -5; since this is NOT greater than 1, the product of all three is NOT greater than any of the numbers. This reasoning can be extended to four or more numbers. For 4 numbers: If the product of all three numbers OTHER than the largest one is GREATER than one, then the product of ALL FOUR numbers is greater than ANY of them.
It is positive. Any product of an even number of negative numbers will be positive, regardless of how many positive numbers you have. Similarly any product of an odd number of negative numbers will be negative, regardless of how many positive numbers you have.
How about: 2*3*5 = 30 which is the product of the 1st three prime numbers
"The sum of a number and three times another number is 18. find the numbers if their product is a maximum?"
If all three numbers are positive then the product obviously has to be positive. If TWO of the three numbers are negative, then the product is also positive. But if exactly ONE of the three numbers is negative or if all THREE are negative, then the product must be negative. In general, a product of numbers is negative if an ODD NUMBER of the terms is negative.
If zero is counted as a whole number, then the first three whole numbers are zero, one and two and the product of ANY series containing zero is ZERO. If, on the other hand, only non-zero numbers are considered, then the series is one, two and three and the product is six.
No.
No
Negative because product of 47 negative numbers is negative and product of three positive number is Positive , so negative*positive = Negative.
four
"Either" is used for two. I'll assume that you mean "larger than ANY of them". The following applies to ANY real numbers.For TWO numbers, the product is larger than either of them if both numbers are greater than one. For THREE numbers, the product is larger than any of them if the two numbers OTHER than the largest number have a product greater than one. For example: 0.5, 3, 5 The largest number here is 5; the product of the OTHER two is 0.5 x 3 = 1.5. Or here is an example with integers: -5, -3, 10 The product of the "other two" numbers is 15, which is larger than one - so the product of all three is larger than the largest number (and therefore, larger than ANY of them). Another example: -5, 1, 10 The product of the two numbers OTHER than the largest is -5 x 1 = -5; since this is NOT greater than 1, the product of all three is NOT greater than any of the numbers. This reasoning can be extended to four or more numbers. For 4 numbers: If the product of all three numbers OTHER than the largest one is GREATER than one, then the product of ALL FOUR numbers is greater than ANY of them.
No.
No. 15 is the product of two prime numbers: 3 and 5
It is positive. Any product of an even number of negative numbers will be positive, regardless of how many positive numbers you have. Similarly any product of an odd number of negative numbers will be negative, regardless of how many positive numbers you have.
How about: 2*3*5 = 30 which is the product of the 1st three prime numbers