Input a number to determine if it's a sphenic number, or specify a range to generate all sphenic numbers within it.
Sphenic Number Check or Generate
Result
Result
What Is a Sphenic Number?
A sphenic number is a positive integer that is the product of exactly three distinct prime numbers. For example, 30 = 2 × 3 × 5 is a sphenic number because it is the product of three different primes. Sphenic numbers are unique in their composition, making them an interesting subject in number theory.
How to Determine If a Number Is a Sphenic Number
Prime Factorization: Break down the number into its prime factors. Identify all the prime numbers that multiply together to give the original number.
Check the Number of Distinct Prime Factors: Ensure that there are exactly three prime factors and that all of them are different. If a prime number is repeated, the number is not sphenic.
Result Determination: If the number has three distinct prime factors, it is a sphenic number. If it has fewer or more than three, or if any prime factor is repeated, it is not a sphenic number.
Examples
Example 1: Is 30 a Sphenic Number?
Solution:
Prime Factorization: 30 = 2 × 3 × 5
Number of Prime Factors: 3 (2, 3, 5), all distinct.
Result: 30 is a sphenic number.
Example 2: Is 60 a Sphenic Number?
Solution:
Prime Factorization: 60 = 2 × 2 × 3 × 5.
Number of Prime Factors: 3 (2, 3, 5), but 2 is repeated.
Result: 60 is not a sphenic number.
Example 3: Is 1030 a Sphenic Number?
Solution:
Prime Factorization: 1030 = 2 × 5 × 103.
Number of Prime Factors: 3 (2, 5, 103), all distinct.