A Multiplication Based Logic Puzzle

494 is the hypotenuse of one Pythagorean triple: 190-456-494. What is the greatest common factor of those three numbers?

  • 494 is a composite number.
  • Prime factorization: 494 = 2 x 13 x 19
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8. Therefore 494 has exactly 8 factors.
  • Factors of 494: 1, 2, 13, 19, 26, 38, 247, 494
  • Factor pairs: 494 = 1 x 494, 2 x 247, 13 x 38, or 19 x 26
  • 494 has no square factors that allow its square root to be simplified. √494 ≈ 22.22611


Years ago my husband and I wanted to research his family tree so I decided to visit the Family History library in downtown Salt Lake City on 8 April 2010. At that time we knew the names of his four grandparents, his eight great-grandparents, and one great-great-grandfather. We knew all of these people were born in Hungary. The information we had was that two of his grandparents were born in a little town called Gyoma in what is now eastern Hungary. We had no idea where his other two grandparents were born. This day was the first time I ever looked at any Hungarian genealogical records. I knew maybe ten words in Hungarian, and I had never even seen similar records in English.

The records were recorded on microfilm which were sorted into Roman Catholic, Reformed Hungarian, Lutheran, and Jewish records. I had no idea what religion his ancestors were, but based on the number of microfilms available for each religion in Gyoma, chances were that they belonged to the Reformed Church. I found a microfilm with Kereszteltek (christening) records from 1883-1895. A volunteer showed me how to put the microfilm on a the reader, and I started looking. I made notes of which records interested me. It was so exciting to find records that had names of people I had heard stories about. It was my intention to photocopy as many family records as I could, scan them into my home computer, and email them to my son, David, who speaks Hungarian fluently but lived in Qatar at the time. However, when I went to make copies, I was pleasantly surprised to learn that I could actually copy the records directly onto a flash drive!

I emailed my son that the five hours I spent at the family history library were well spent. I didn’t find any of the christening records I was expecting to find but found about thirteen records of his ancestor’s siblings. I attached the records to the email and waited for morning to arrive in Qatar so he could reply.

The next day he emailed me back, “I only had time to look at the first four (records). I’ll check the rest later. I’ve written some notes below, but I should let you know that you basically just found four people who aren’t related to us.” He then wrote in English what each of the records said.

Later he emailed me, “To continue the bad news, Now that I look at all of them, I can see that they (the great-grandparents) are all listed as godparents. This should explain why you didn’t find much of what you were actually looking for. Now you know, and should be able to look for names in the right column.”

He sent me translations of the page headings so I wouldn’t go wrong in the future. The christening records were two pages wide. Here are the headings with his translations for the first page:

And here are the headings with translations for the 2nd page.

So there you have it. Since I knew so little Hungarian and so little about how christening records are organized, I thought the godparents were the parents.

I had to wait a whole week before I could go back to the library, but this first visit was not a total bust. We still learned a few things about my husband’s great-grandfather, Dániel Finta, that we didn’t know before. We learned that he worked in a factory making shoes because his profession was given next to his name on at least one record. We learned that Dániel was asked on several occasions to be a godfather. Sometimes his wife was the godmother with him, and sometimes his mother was. Because I found these records we now knew his mother’s name, Sára Bíró, as well. We also learned that Dániel belonged to the Reformed Church and his wife, Emília Pribelszky, was Lutheran.

I was grateful for what we had learned and anxious to return again.

How successful were you the first time you looked into your family history? If you were discouraged, please give it another try. It is so worth it. If you were successful, you know exactly what I mean.


Comments on: "494 My First Microfilm Treasure Hunt" (1)

  1. […] Find the factors is an interesting blog, where you can see the beauty of numbers together with other interesting things. I like the idea that for every post she talks about the number of the post (thus you get a lot of number facts). To understand the process better, you can read her last post: 494 My First Microfilm Treasure Hunt. […]


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