Perfect squares have an odd number of factors. There are 31 perfect squares less than 1000.
Literally every single even number less than 1000 is a composite number other than 2 which is prime.
Every second number greater than 2 is an even number.
512 = 29 or 768 = 28*3 have 9 prime factors each.
By definition, a prime number has exactly two factors. So, there are no prime numbers with exactly three factors.
It's relatively easy to show that there are no numbers less than 1000 that are made of more than 4 different prime factors. The 5 smallest primes are 2, 3, 5, 7 and 11, and 2x3x5x7x11=2310. If the smallest 5 different primes multiplied together gives a product greater than 1000, then any other combination of 5 different primes would yield an even bigger number. So any number less than 1000 that is comprised of different prime numbers must only have 4 prime factors. So the smallest number that's a product of 4 different primes is 210 (=2x3x5x7), but there are several other numbers less than 1000 that are made of 4 different prime factors. A complete list follows: 2x3x5x7 = 210 2x3x5x11 = 330 2x3x7x11 = 462 2x5x7x11 = 770 2x3x5x13 = 390 2x3x11x13 = 858 2x3x5x17 = 510 2x3x7x17 = 714 2x3x5x19 = 570 2x3x7x19 = 798 2x3x5x23 = 690 2x3x7x23 = 966 2x3x5x29 = 870 2x3x5x31 = 930
There are 31 numbers less than 1,000 which have an odd number of factors. They are: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961.
1000 more is 577233 1000 less is 575233
210 has 4, which is the maximum possible. There are other numbers with 4 different prime factors.
577233 and 575233 respectively
11
840
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.
There are 12 numbers less than 150 which have an odd number of factors: 1,4,9,16,25,36,49,64,81,100,121,144.
If you take away 1000 from 503000019 you get 502999019.If you add 1000 to 503000019 you get 503001019.
There are four odd numbers less that 100 that have 6 factor. This does not compare with even numbers that have 12 factors!
Literally every single even number less than 1000 is a composite number other than 2 which is prime.
1000.0