Math and Arithmetic

# Are all numbers divisible by 3 and 4 divisible by 6?

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###### 2011-01-26 06:57:13

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.

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## Related Questions

All numbers that are multiples of 12 are divisible by both 3 and 4.

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.

All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.

All numbers that are divisible by 6 are even numbers whose digits add up to 3 or a multiple of 3. Example : 284 is not wholly divisible by 6 as although it is even, its digits total 2 + 8 + 4 = 14 which is not divisible by 3. 282 is divisible by 6 as it is even and its digits total 12 which is divisible by 3.

No. 26 for instance the sum of the digits is 8 but not divisible by 4. 32 the sum of the digits is 5 but divisible by 4 The rules for some other numbers are 2 all even numbers are divisible by 2 3 The sum of the digits is divisible by 3 4 The last 2 numbers are divisible by 4 5 The number ends in a 0 or 5 6 The sum of the digits is divisible by 3 and is even 7 no easy method 8 The last 3 numbers are divisible by 8 9 The sum of the digits is divisible by 9

All numbers that are divisible by 8 and 12 would also be divisible by 4.

2: 2,4,6,8,10,12,14,16,18,20...4: 4,8,12,16,20,24,28,32,36,40...Half of all numbers divisible by 2 are divisible by 4.All numbers divisible by 4 are divisible by 2.

All even numbers are divisible by 2, but all even numbers are not divisible by 4. Some that aren't are 6, 10, 14, 18, 22...

They are divisible by 2, 3, 4, 5, 6, 10, 12, 15, 30 and 60 at least.

No since only numbers in which its sum can be divisible by 3 is divisible by 3. 2 + 4 + 4 is 10, and 10 is not divisible by 3.

no only divisible by 2 10 is an even number but is not divisible by 4 for example.

0,12,24,36,48,60,72,84, and 96 are the numbers between 0 and 100 that are divisible by both 3 and 4.

To know if a number is composite without listing its factors, you can use these rules:All numbers that end with 2, 4, 6, 8, and 0 (even numbers) are divisible by 2.If the sum of the digits in a number is divisible by 3, the number is divisible by 3.If the last two digits are divisible by 4, the number is divisible by 4.All numbers that have 5 in the one's place are divisible by 5.If a number is divisible by 2 AND is divisible by 3, it is divisible by 6.If the last 3 digits of a number are divisible by 8, the number is divisible by 8.If the sum of the digits of number is divisible by 9, the number is divisible by 9.If a number ends wuth 0, the number is divisible by 10.

For example you have two numbers 4 and 5 and we add them the result is 9 which is also divisible by 3 if we divide it by 3 the result will be. So it means that total/addition of all the numbers which after addition can be divisible by 3.

No prime numbers are only divisible by one and by themselves.

No. The reverse is true, but 12 is divisible by 4 and not by 8.

Well, if you really mean divisible by 4 then the answer is 100% that is probability 1.00. On the other hand, if you mean evenly divisible by 4, then in the numbers 1-12 there are 3 numbers evenly divisible by 4 (4, 8, 12) since there are 12 numbers then the probaqbility of a number divisible by 4 is 3/12 = 0.25

No, but I suspect you want to know if 186624 is divisible by those numbers. Out of that list, 186624 is divisible by all but 5.

4 has an infinite number of multiples, all of them divisible by 4, because numbers don't stop.

Numbers divisible by 8 will all be even. They will all be divisible by 4 and again by 2, and will all be divisible by 2 and by 2 again and by 2 again.2,7,9,6,9

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