answersLogoWhite

0


Best Answer

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

User Avatar

Wiki User

16y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Which number under 1000 has the most different prime factors?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

What prime number under 1000 has the most different prime factors?

Ur mu m Isn't this great? She's had sooooo many children, they are all her factors


What is the highest number you can make under 100 with 2 different prime factors?

5 x 19 = 95


Which number under 100 has the most prime factors?

1


How many number under 10 have 2 factors?

There are 4 prime numbers under ten.


How do you solve the largest prime number of 100?

The prime factors of 100 are 2 and 5; the largest of these is 5. The largest prime number under 100 is 97.


Is 91 a prime number under 100?

91 is not a prime number. 91 is a composite number having the factors 1, 7, 13, and 91.


What number under 300 has the most unique prime factors?

Here is how you can calculate that: Multiply different prime numbers together, until your product exceeds the number 300. Then, you go back one step.


A number that is not prime or composite?

A number that isn't prime or composite is 1 its only factor is 1 (1 x 1).For a number to be prime, it should have two factors: 1 and itself.For a number to be composite, it should have more than two factors.1 has under two factors, which therefore makes it a "special number".


What numbers under 100 have 3 different prime factors?

30, 42, 66, 70 and 78.


What are 3 numbers under 100 that have exactly 4 factors?

Such a number would either have to be a perfect cube of a prime number, such as 33 = 27 (the only one in the specified range), or the product of exactly two different prime factors, such as 2 x 3, 2 x 5, 3 x 31, etc.


What prime number under 20 can be expressed as the sum of three different prime numbers?

They are: 3+5+11 = 19


What is the largest prime number to check for prime numbers under 100?

the largest prime number under 100 is 97