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

JordanJordan
Looking for a career mentor? I've seen my fair share of shake-ups.
Chat with Jordan
MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga

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