Seven years ago today at 2:11 in the morning, I published my first blog post. It featured a Find the Factors 1 – 10 puzzle with only perfect square clues. In honor of that first post, I publish this puzzle, also with only perfect square clues. This one looks like an exclamation point because I have enjoyed creating puzzles and writing these posts for you so much these seven years!
How do you solve the puzzle? Use logic to write the numbers from 1 to 10 in both the first column and the top row so that the puzzle functions like a multiplication table.
Factors of 1546:
1546 is a composite number.
Prime factorization: 1546 = 2 × 773.
1546 has no exponents greater than 1 in its prime factorization, so √1546 cannot be simplified.
The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1546 has exactly 4 factors.
The factors of 1546 are outlined with their factor pair partners in the graphic below.
More about the Number 1546:
1546 is the sum of two squares:
39² + 5² = 1546.
1546 is the hypotenuse of a Pythagorean triple:
390-1496-1546, calculated from 2(39)(5), 39² – 5², 39² + 5².
It is also 2 times (195-748-773)
I continue to be very grateful to WordPress and the WordPress community for making blogging and publishing easy and enjoyable. I am also very grateful to my readers who have done so much to make this blog grow.
I’m a lot busier now than I was five years ago. Besides blogging, I have a full-time job and a part-time job. I like both of these jobs because I like helping students understand mathematics better. Sometimes I don’t have the time I would like to work on my blog. Nevertheless, I still have blogging goals I want to reach so lately I find myself playing catch-up more often than not.
Now I’ll write a little about the number 1270:
1270 is a composite number.
Prime factorization: 1270 = 2 × 5 × 127
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 × 2 × 2 = 8. Therefore 1270 has exactly 8 factors.