## A Multiplication Based Logic Puzzle

### 847 Sending Love to My Sister in Louisianna

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

My sister, Sue, lives in Louisiana. Several years ago Katrina upset her life, and now Harvey is pounding at her door. I have not heard from her since yesterday when she posted this dreary picture on facebook with the caption, “Flooded at my street.”

Sue, I hope you are okay. If you need a diversion, I hope this puzzle helps at least a tiny bit. I made it just for you. If you need someplace to stay, you can stay with me and my family. We send lots of love and prayers your way.

We also have a son, daughter-in-law, and two grandchildren who live in the Houston area. They are doing okay, but many of their friends are struggling. We pray for them as well.

After the freightening wind died down some, my daughter-in-law posted this picture with the caption, “Day 2 of Hurricane Harvey: We found a Craw-Dad in the back yard!”

My daughter-in-law later posted, “For those of you who are not in Houston I wanted to give you an update. We are located in Kingwood which is northeast of Houston. We have had rain since last Friday and many of our lakes, rivers and bayous are flowing out of their banks. Our home has been very blessed to be in a neighborhood where the rain water is draining nicely, so far. But many of our friends are not as lucky and have had to evacuate due to high water in their homes. We had one small leak in our kitchen, but were able to cover it and stop the dripping. We feel very blessed, but also very concerned for our friends and neighbors. Houston could use your prayers.”

I would like to add that Louisiana and several other towns and cities in Texas could use our prayers, help, and donations.

Now I’ll write a little about the number 847:

844, 845, 846, 847, and 848 are the smallest five consecutive numbers whose square roots can be simplified.

847 is palindrome 1011101 in BASE 3 because 3⁶ + 3⁴ + 3³ + 3² + 3º = 847.

847 is also 700 in BASE 11 because 7(11²) = 847.

Stetson.edu informs us that 847 is the sum of the digits of 2¹⁴ – 1, the 14th Mersenne prime. Since its digits sum to 847, that prime number has to be at least 95 digits long!

• 847 is a composite number.
• Prime factorization: 847 = 7× 11 × 11, which can be written 847 = 7 × 11²
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 × 3  = 6. Therefore 847 has exactly 6 factors.
• Factors of 847: 1, 7, 11, 77, 121, 847
• Factor pairs: 847 = 1 × 847, 7 × 121, or 11 × 77
• Taking the factor pair with the largest square number factor, we get √847 = (√121)(√7) = 11√7 ≈ 29.1032644