- Divisible is typically used to test whether n is divisible by m.
- n is divisible by m if n is the product of m by an integer.
- Divisible[n,m] is effectively equivalent to Mod[n,m]==0.
- Divisible[n, m] returns False unless n and m are manifestly divisible.
- Divisible[n,m] can be entered as .
- can be entered as \[Divides] or divides.
Examplesopen allclose all
Divisible works over integers:
Symbolic forms of numeric quantities:
Divisible threads elementwise over lists:
Basic Applications (3)
Number Theory (5)
Recognize Wieferich primes, prime numbers p such that divides :
There are only two known Wieferich primes:
Let be all numbers of the form :
Check that the product of two numbers is still in :
Recognize Hilbert primes, prime numbers that have no divisors in other than and themself:
Find the first Hilbert primes:
Find two representations of a number as the sum of two squares:
Find a divisor of the number by computing the GCD of and the number:
Find another divisor by computing the GCD of and the number:
An integer is divisible by if the sum of its digits is divisible by :
An integer is divisible by if the alternating sum of the digits is divisible by :
Properties & Relations (7)
If is an integer, then is divisible by :
If is divisible by , then the greatest common divisor GCD of them is :
If and are relatively prime, then is not divisible by :
If the prime factorization of an integer has the form , then the number of its divisors is :
Use Divisors to find all divisors of an integer:
PrimeNu gives the number of distinct prime divisors:
Possible Issues (2)
Interactive Examples (1)
Wolfram Research (2007), Divisible, Wolfram Language function, https://reference.wolfram.com/language/ref/Divisible.html.
Wolfram Language. 2007. "Divisible." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Divisible.html.
Wolfram Language. (2007). Divisible. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Divisible.html