Print the puzzles or type the solution on this excel file: 12 factors 843-852

I knew that 852 was divisible by 3 as soon as I typed it in a straight line on the number pad. Any 3 digit number that lies on a straight line on a number pad or a phone dial pad is divisible by 3. And in case you’ve ever wondered why the numbers on a number pad or calculator and the numbers on a phone dial pad are reversed, ABC News has the answer.

852 is **7****05** in BASE 11, and it is **5****07** in BASE 13.

852 is palindrome 1E1 in BASE 23 (E is 14 base 10) because 1(23²) +14(23¹) + 1(23º) = 852.

852 is the sum of consecutive prime numbers 421 and 431.

852 is also the 24th pentagonal number because (3⋅24² – 24)/2 = 852

- 852 is a composite number.
- Prime factorization: 852 = 2 × 2 × 3 × 71, which can be written 852 = 2² × 3 × 71
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 852 has exactly 12 factors.
- Factors of 852: 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
- Factor pairs: 852 = 1 × 852, 2 × 426, 3 × 284, 4 × 213, 6 × 142, or 12 × 71,
- Taking the factor pair with the largest square number factor, we get √852 = (√4)(√213) = 2√213 ≈ 29.189039

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