To determine how many ways 14630 can be expressed as a product of two numbers, we first need its prime factorization. The prime factorization of 14630 is (2 \times 5 \times 1463). The number of divisors can be calculated from the exponents of the prime factors; since (2^1, 5^1, \text{ and } 1463^1) each have an exponent of 1, the total number of divisors is ((1+1)(1+1)(1+1) = 2 \times 2 \times 2 = 8). Each pair of divisors ( (d, \frac{14630}{d}) ) gives a product of 14630, so the number of unique pairs is half of the total number of divisors, leading to 4 ways to express 14630 as a product of two numbers.
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.
There are 25 such numbers.
Two
4
Oh, dude, that's an easy one. So, you can write any number less than 1000 as the product of 3 consecutive numbers, right? Well, except for the numbers at the beginning and end because they don't have 3 numbers before or after them to multiply with. So, that leaves us with 997 numbers. Easy peasy lemon squeezy.
15
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.
There are infinitely many such product pairs.
There are 25 such numbers.
Two
4
This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.
Oh, dude, that's an easy one. So, you can write any number less than 1000 as the product of 3 consecutive numbers, right? Well, except for the numbers at the beginning and end because they don't have 3 numbers before or after them to multiply with. So, that leaves us with 997 numbers. Easy peasy lemon squeezy.
Six Numbers; 1,75, 5, 15, 25, 3
two
-21
39!