Venn Diagram Pies:
In the United States many people celebrate pi day. This year it will be one hour shorter as we move to Daylight Saving Time. Since it will be on a Sunday, it might not get as much attention in school. Do we make too much of a deal about the number pi? It’s about 0.02 less than √10, an important, yet less-known number. I compare the two numbers in this Venn diagram:
We ought to take advantage of any reason to celebrate anything and everything in mathematics. I will be making some kind of pie to celebrate pi day, and I hope you do the same,
Now let’s move on to the ….
Factors of 1613:
- 1613 is a prime number.
- Prime factorization: 1613 is prime.
- 1613 has no exponents greater than 1 in its prime factorization, so √1613 cannot be simplified.
- The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1613 has exactly 2 factors.
- The factors of 1613 are outlined with their factor pair partners in the graphic below.
How do we know that 1613 is a prime number? If 1613 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1613. Since 1613 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, or 37, we know that 1613 is a prime number.
More about the Number 1613:
1613 is the sum of two squares:
38² + 13² = 1613.
1613 is the hypotenuse of a Pythagorean triple:
988-1275-1613, calculated from 2(38)(13), 38² – 13², 38² + 13².
Here’s another way we know that 1613 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 38² + 13² = 1613 with 38 and 13 having no common prime factors, 1613 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1613. Since 1613 is not divisible by 5, 13, 17, 29, or 37, we know that 1613 is a prime number.