IS 91 A PRIME NUMBER?

[jmqff]

...number theorists will note that 91 =

100 - 9, a difference of two squares,

hence 91 = (10+3)(10-3), or 13 x 7.

[HAMLETOIS]

I can see how I can use this logic with other composite numbers. Thanks. Here is another way to say 12 is composite.

Example: 16 - 4 = 12 = (4 + 2 = 6) ( 4 - 2 = 2) = 6 • 2 = 12

I can see that the prime factorization of 12 is 2 • 2 • 3 = 12

and this is enough to convince me that 16 is not prime.

Can we say that every composite number is a difference of two squares? How about 6?

[HAMLETOIS]

I am also very astonished how this rule for the divisibility of 7 works. I should continue to use it whenever I need to see if a number is a multiple of seven. Thanks for commenting on this video.

[talalikambo]

Wow, clever! I had never seen this before. I checked it with larger numbers, and the steps are the same:

(1) Multiply the last number by 2.

(2) Subtract this product from the previous numbers.

(3) If the difference is divisible by 7, so is the whole number.

(You can also take the difference and run it through the same steps again.)

[lsefia]

@talalikambo does this rule only work for 2 digit numbers?

[talalikambo]

@lsefia No, it works for larger numbers as well.