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If this is a T-F question, the answer is false. It is true that if a number is divisible by 6, it also divisible by 3. This is true because 6 is divisible by 3. However, the converse -- If a number is divisible by 3, it is divisible by 6, is false. A counterexample is 15. 15 is divisible by 3, but not by 6.

It becomes clearer if you split the question into its two parts.

A number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2.

A number is divisible by 6 only if it is divisible by 3? True.

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โˆ™ 2012-09-25 04:47:31
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Q: A number is divisible by 6 if and only if it is divisible by 3?
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Is it true or false that a number is divisible by 6 if and only if it is divisible by 3?

False. The question consists of two parts: - a number is divisible by 6 if it is divisible by 3? False. It must also be divisible by 2. - a number is divisible by 6 only if it is divisible by 3? This is true but the false part makes the whole statement false.


What number is divisible by 6 but not 3?

There is no such number. Since 6 is divisible by 3, then any number that is divisible by 6 automatically has to be divisible by 3.


What is a 4-digit number that is divisible by only 6 and 9?

There is no number that is divisible by only 6 and 9 because any number is divisible by 1 and itself. Furthermore, any number that is divisible by 6 MUST be divisible by 2 as well as 3 - so only 6 is impossible.


Is this biconditional statement true A number is divisible by 6 if and only if it is divisible by 3?

How can the following definition be written correctly as a biconditional statement? An odd integer is an integer that is not divisible by two. (A+ answer) An integer is odd if and only if it is not divisible by two


What 2 digit numbers are divisible by 3 but not by 6?

Since 3 is a factor of 6, any number divisible by 6 is also divisible by 3. But since 2 is also a factor of 6, then any number divisible by 6 must also be divisible by 2. This means that any number divisible by 6 is an even number. So if a number is odd and it is divisible by 3, then it is not divisible by 6. For example, 12 is divisible by 3, but since it is even, it is also divisible by 6. But 15 is divisible by 3, and it is odd, so it is not divisible by 6.


What number is divisible by 6 also a multiple of 3?

As 6 is divisible by 3, ANY dumber divisible by 6 is also therefore divisible by 3. Any number divisible by 3 is ALSO a multiple of 3.


What numbers are not divisible by 6?

These numbers are not evenly divisible by 6: Any number smaller than 6. Any odd number (not divisible by 2). Any number not divisible by 3. If a number is divisible by both 2 and 3, it is divisible by 6.


What is the divisible by 6?

If a number is divisible by 2 and 3, it is divisible by 6.


What is the divisible of 6?

if a number is divisible by 2 and 3 then its divisible by 6


Is 138 divisible by 6?

138 is divisible by 6. Any number is divisible by 6 if it is an even number that also is divisible by 3.


What are the divisibility rule for 6?

To be divisible by 6, the number must be divisible by both 2 and 3:To be divisible by 2 the last digit must be even, ie one of {0, 2, 4, 6, 8};To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3.As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {3, 6, 9} is the original number divisible by 3.If the number is not divisible by 2 or 3 (or both) then the number is not divisible by 6.examples:126Last digit is even so it is divisible by 2 1 + 2 + 6 = 9 which is divisible by 3, so it is divisible by 3→ 126 is divisible by both 2 and 3, so it is divisible by 6124Last digit is even so it is divisible by 2 1 + 2 + 4 = 7 which is not divisible by 3, so it is not divisible by 3→ 126 is divisible by 2 but not divisible by 3, so it is not divisible by 6123Last digit is not even so it is not divisible by 2 We can stop at this point as regardless of whether it is divisible by 3 or not, it will not be divisible by 6. However, for completeness:1 + 2 + 3 = 6 which is divisible by 3, so it is divisible by 3→ 123 is divisible by 3 but not divisible by 2, so it is not divisible by 6121Last digit is not even so it is not divisible by 2 We can stop at this point as regardless of whether it is divisible by 3 or not, it will not be divisible by 6. However, for completeness:1 + 2 + 1 = 4 which is not divisible by 3, so it is not divisible by 3→ 121 is not divisible by either 2 or 3, so it is not divisible by 6


If a number is divisible by 3 then it is divisible by 6?

Not always as for example 81 is divisible by 3 but not by 6


What is the rule for multiples of 6?

If a number is divisible by 2 (an even number) and 3 (the sum of the digits is divisible by 3) then the number is divisible by 6.


Is 293 divisible by 6?

It is not divisible by 6. Note:If a number id divisible by 6 then it must be divisible by both 2 and 3.The above number is not divisible by 2 and 3 either.


Are all even numbers divisible by 6?

Not all even numbers are divisible by 6. These numbers are not evenly divisible by 6: Any number smaller than 6. Any number not divisible by 3. If a number is divisible by both 2 and 3, it is divisible by 6.


If the number is divisible by 2 and 3 the whole number is divisible by?

It is divisible by 6


What number is divisible by 6 but not divisible by 2 and 3?

There is no such number.


How do you know if a number is divisible is by 3?

if one of its factors are a 3 or after dividing a number by 3, their are no remainders There is also another trick: add all of the digits of the number together. The original number is divisible by 3 if and only if the sum of the digits is divisible by 3. For example: 321 is divisible by 3 because 3+2+1=6 and 6 is divisible by 3. 322 is not divisible by 3 because 3+2+2=7 and 7 is not divisible by 3.


If a number is divisble by both 2 and 3 is it divisible by 6?

Any number that is divisible by both 2 and 3 is divisible by 6.


Is 5232 divisible by 6?

Since 5232 is divisible by both 2 and 3, it is divisible by 6.A number must be divisible by both 2 and 3 to be divisible by 6.The number 5232 is even, so it is divisible by 2.If you add the individual digits in the number (5+2+3+2=12) you get a number that is divisible by 3, meaning the original number (5232) is also divisible by 3.


A number is divisible by 6 if it is divisible by what numbers?

2 and 3Today, people don't explain why a number has to be divisible by 2 and 3 to be divisible by 6 or how it works.


What is the test of divisibility for 6?

A number is divisible by 6 if the number is divisible by 2 AND 3.


How can you tell if a number is divisible by 6?

If the number is divisible by 2 and 3, it can also be divided by 6.For example - 12126 is divisible by 2 and 3 and6Divide it by 6 and see if you get a whole number.


Is 483 divisible by 6?

No. 483 is not divisible by 6.A number is divisible by 6 if it is divisible by both 2 and 3.It is divisible by 2 if it is even and it is divisible by 3 if the sum of the digits is a multiple of 3.483 is not divisible by 6 since it is not divisible by 2 although it is divisible by 3.


What does a number have to have to be divisible by 6?

It has to be divisible by 2 and 3 to be dividible by 6.

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