Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Prime Numbers help. They say that a prime number is any number that's divisible by itself and one?

But surely every number is divisible by

itself to give 1 and by 1 to give itself.

For example,

175/175 = 1 and 175/1 = 175

So, can someone please tell me what it is that I am not understanding?

How come 3 is a prime number and 4 not?

4 is divisible by itself to give 1 and 4 is divisible by 1 to give 4. as far as I can every number including decimal ones are all prime numbers based on this definition.

Update:

Thank you for all your answers, I now know what a prime number is. it feels a little stupid i could not see such a simple thing before. Thanks to you all once again.

Update 2:

The keyword being ONLY

Relevance
• 1 month ago

A prime is a whole number divisible by ONLY itself and one.

175 is not prime, because it can be divided by 5

4 is not prime, because it can be divided by 2.

3 is prime, because it can be divided by 1 and 3, and NO OTHER NUMBERS.

(By "divisible", I mean in whole numbers only, without remainder.)

• Hockey
Lv 6
1 month ago

4 can be divided by 1,2 and 4 and will return a whole number every time. However, 3 can be divided by 1 and 3 and return a whole number, but when divided by 2 the division will return a fraction and not a whole number.

• Lisa A
Lv 7
1 month ago

They don't say that. You were listening wrong. They say that a prime number is any number that's divisible ONLY by itself and one, and no other numbers.

• 1 month ago

You're almost there, but a prime number is a *positive integer* that has *exactly two* positive divisors, namely 1 and itself.

Negative numbers are excluded.

0 is excluded

1 only has 1 factor and is excluded

2 has exactly 2 factors (1 and 2) --> prime

3 has exactly 2 factors (1 and 3) --> prime

4 has *3* factors (1, 2 and 4) --> composite

5 has exactly 2 factors (1 and 5) --> prime

...

175 has *6* factors (1, 5, 7, 25, 35, 175) --> composite

• 1 month ago

The definition is if a number is ONLY divisible by 1 and itself.

3 is prime because the only divisors are 1 and 3.

4 is not prime because the divisors are 1, 2, and 4.

• 1 month ago

To answer your question, you need to read the definition of prime.  The other answers are close, but you need to look up the definition of the term as you find it in your text book.  The one I grew up with says:

A prime number is a positive integer greater than one, that has no positive integer factors except one and itself.

So 0 and 1 are not prime

2 is the only even prime

3 is prime

4 is not because 2*2 = 4 and neither of these factors is 4.

Negative numbers are not prime.

Fractions are not prime

Irrational numbers (e.g. sqrt(2) ) are not prime.

Hope this helps.

• 1 month ago

No...you've got what a prime number is wrong.

A prime number is a whole number that is only divisible by itself and by one. In both cases the result must also be a whole number. 1, 3, 5, 7, 11, 13 are primes. Only 5 and 1 will divided into 5 for example.

Your 175 is divisible by itself, sure, but it's also divisible by 5 and 25 right off hand (there might be more but I'm illustrating the process). So it's not a prime.

How about 15...is it a prime number? Is it divisible by a number other than itself and one?

Yep...both 3 and 5 will divide into it. So it's not a prime.

• Anonymous
1 month ago

Re-read the definitions of a prime number. A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. 175 = 5x5x7 so it is not a prime.