### Today’s Puzzle:

Use logic to write each number from 1 to 12 in both the first column and the top row so that those numbers are the factors of the given clues.

### Factors of 1733:

- 1733 is a prime number.
- Prime factorization: 1733 is prime.
- 1733 has no exponents greater than 1 in its prime factorization, so √1733 cannot be simplified.
- The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1733 has exactly 2 factors.
- The factors of 1733 are outlined with their factor pair partners in the graphic below.

**How do we know that ****1733**** is a prime number?** If 1733 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1733. Since 1733 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, or 41, we know that 1733 is a prime number.

### More About the Number 1733:

1733 is the sum of two squares:

38² + 17² = 1733.

1733 is the hypotenuse of a Pythagorean triple:

1155-1292-1733 calculated from 38² – 17², 2(38)(17), 38² + 17².

Here’s another way we know that 1733 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 38² + 17² = 1733 with 38 and 17 having no common prime factors, 1733 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1733. Since 1733 is not divisible by 5, 13, 17, 29, 37, or 41, we know that 1733 is a prime number.

1733 is also the difference of two squares:

867² – 866² = 1733.

That means 1733 is also the short leg of the Pythagorean triple calculated from

867² – 866², 2(867)(866), 867² + 866².

1733 is a palindrome in three bases:

It’s 2101012 in base 3 because

2(3⁶) +1(3⁵) + 0(3⁴) + 1(3³) + 0(3²) +1(3¹) + 2(3⁰) = 1733,

It’s 565 in base 18 because 5(18²) + 6(18) + 5(1) = 1733, and

it’s 4F4 in base 19 because 4(19²) + 15(19) + 4(1) = 1733.

The next fact I learned from Twitter:

#math: 1733 is the smallest prime that contains exactly 6 smaller primes as substrings.#NumbersFacts #fatcs #number

more facts ? get the app now !

👇 👇 👇https://t.co/m48RTdfYlv— NumbersFacts (@Numbers_Facts_) February 18, 2022

What prime numbers can be made with the digits of 1733?

**3**, **7**, 13, **17**, 31, 37, 71, **73**, 137, **173**, 313, 317, 331, 337, 373, **733**, **1733**.

The numbers in red are the 6 prime numbers that are substrings of 1733. I made a gif showing those 6 primes: