Prime Factors | Common Divisors | Common Multiples | Divisors | Radical

Find Numbers with Common Divisors

In a span of numbers, those with up to five defined divisors will be calculated. Please enter a span and up to five divisors to search for. All numbers within that span with at least one and up to five divisors will be calculated. As divisors, positive and negative integer numbers are counted. If the span or the numbers within the span are very high, the calculation might take a while.

Amount of numbers and values, which have 1-5 of the divisors above
5 divisors:
4 divisors:
3 divisors:
2 divisors:
1 divisor:

All:

Example shows the numbers in the range 1 to 100 that have 2, 3, 4, 5, or 6 as factors. A single number, 60, has all five of these factors. Nine numbers have exactly four factors, ten have exactly three factors, 19 have exactly two factors, and 35 have only one factor. The total amount of numbers that have at least one of the five given factors is 74.

A factor is a non-zero integer by which another integer is divisible without a remainder. For example, 3 is a factor of 6 because 6 divided by 3 gives 2 without a remainder. A natural number has at least two factors: one and itself. If it has no other factors, then it is a prime number. However, most natural numbers have more than two factors.
Two or more numbers can have common factors. One is always a common divisor of whole numbers, so entering 1 as a divisor doesn't make much sense, and the same applies to -1. Here, we're looking for numbers with specific common divisors. The term common divisors is often used as the greatest common divisor, gcd. However, this is different, as this is not looking for a limited number of divisors, but rather all possible divisors.