Factoring and Multiples
Prime Numbers

# Why do prime numbers have a remainder of 1 or 5 when divided by 6?

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###### 2010-03-14 02:36:58

If the number has a remainder of 2 or 4 when divided by 6, it is an even number, so it is not Prime number.

6n + 2 = 2 (3n + 1), so it is divisible by 2.

6n + 4 = 2 (3n + 2), so it is divisible by 2.

If the number has a remainder of 3 when divided by 6, it is divisible by 3, so it is not a prime number.

6n + 3 = 3 (2n + 1), so it is divisible by 3.

However, there are two prime numbers that do not have a remainder of 1 or 5 when divided by 6 : 2 and 3

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## Related Questions

A prime number can be divided, without a remainder, only by itself and by 1. Zero and 1 are not prime numbers.

109 is a prime number, therefore the only numbers that can be divided into 109 are:1 and 109."A positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded:The integers 2, 3, 5, and 7 are prime numbers. "-Dictionary.com definition for "prime number".

The definition of a prime number is a number that can only be divided by 1 and itself. Prime numbers can not be divided by anything but 1.

49 can be divided by these numbers without leaving a remainder: 1 7 and 49.

They are the numbers that when divided by 2 leave a remainder of 1

Well i think Prime Numbers are quite important! What A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1

NO. Prime numbers only can be divided by itself or 1, no other numbers. However 16 can be divided by 2,8,4

Prime numbers are numbers that can only be divided by one and itself. The answer is 2,3,5,7,11,13,17,19. 1 is not prime nor composite.

Numbers ending in 0, 2, 4, 6, or 8 can be divided by 2 to give an integer result. This is half of all numbers. The remaining numbers can be divided by 2 but ave a remainder of 1

A composite number is when it can be divided evenly by numbers other than 1 or itself. A prime number can be divided, without a remainder, only by itself and by 1. Therefore, zero is neither a composite, nor a primary number.

prime number-a number that can only be divided by 1 or itself without resulting in a remainder therefore if the product (multiplying) of 2 prime numbers could be divided by either of the prime numbers, 1, and itself. example 2X3=6 6/1=6 6/6=1 6/3=2 6/2=3

Odd numbers can't be evenly divided by 2 because there will always be a remainder of 1

341 is not a prime number. Prime numbers are defined as numbers which can be divided by 1 and themselves. 341 can be divided by 11 and 31 in addition to 1 and iteslf. Hence, 341 is not a prime number.

The answer is 1. The smallest prime is 2 and the greatest prime (of however many digits) must be odd. The remainder of ANY odd number when divided by 2 must be 1.

Prime numbers are numbers that can be divided by by only 1 and itself. 494 can be divided by 2, 247 etc. so it is not a prime number.

Since the remainder is 0 when the numbers are divided by 3, then that number is a multiples of 3. For example, 45/3 = 15 remainder 0 45/4= 11 remainder 1 45/7 = 6 remainder 3

Yes. 18 can be divided by these numbers without a remainder: 1 2 3 6 9 and 18.

46 can be divided by these numbers without leaving a remainder: 1 2 23 and 46.

It means the remainder if any when numbers are divided as for example 49 divided by 6 = 8 with a remainder of 1 leftover

7, 37, 67, 97, 127, and an infinite number of other numbers in this series (starting with 7 and increasing in increments of 30) have a remainder of 1 when divided by 6 and a remainder of 2 when divided by 5.

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