answersLogoWhite

0

Yes. If a number is evenly divisible by both 3 and 4, it will also be divisible by 6.

This is because the prime factor of 3 is [3] -- in other words, 3 is a Prime number -- and the prime factors of 4 are [2, 2].

Thus, any number that is divisible by 3 and 4 will have as part of its prime factors the set [2, 2, 3]. (The smallest such number is 12, which is 2 x 2 x 3.) Since the prime factors of 6 are [2, 3] -- and [2, 3] is a subset of [2, 2, 3] -- then any such number must also be divisible by 6.

Another way to look at it is to note that all numbers which are divisible by both 3 and 4 are also divisible by 12 (which is 3 x 4). Since 12 is divisible by 6, then all multiples of 12 will also be divisible by 6.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

JudyJudy
Simplicity is my specialty.
Chat with Judy
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
ProfessorProfessor
I will give you the most educated answer.
Chat with Professor

Add your answer:

Earn +20 pts
Q: Are all numbers divisible by 3 and 4 divisible by 6?
Write your answer...
Submit
Still have questions?
magnify glass
imp