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.
Still curious? Ask our experts.
Chat with our AI personalities
Rene
Ezra
ProfessorAdd your answer:
Earn +20 pts
What are the divisibility rules for 1 2 3 4 5 6 9 and 10?
All whole numbers are divisible by 1. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Numbers are divisible by 4 if the last two digits of the number are divisible by 4. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. Numbers are divisible by 6 if they are divisible by 2 and 3. Numbers are divisible by 9 if the sum of their digits is equal to 9 or a multiple of 9. Numbers are divisible by 10 if the last digit of the number is 0.
What is a 4 digit number that is divisible 3 and 9?
All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.
Which of the following is divisible by 3 and 6 but is not divisible by 4?
All numbers of the form 6+12x are, for all integer x.
All numbers divisible by 8 and 12 are also divisible by?
All numbers that are divisible by 8 and 12 would also be divisible by 4.
Are all numbers divisible by 9 also divisible by 4?
no, 18 is divisible by 9 but not by 4.
