# 444 and Level 3

What are the factors of 444? I’m not going to tell you to add 4 + 4 + 4 to see if it is divisible by 3 or 9, because it so obvious, there are three 4’s and three of anything is divisible by 3. The only way three of something could be divisible by 9 is if it were 333 or 666 or 999 so 444 is not divisible by 9.

But try adding the digits for a completely different reason: 4 + 4 + 4 = 12. Guess what, 444 can be evenly divided by 12. Many numbers can be divided evenly by the sum of their digits. In recreational mathematics, numbers with this property are called Harshad numbers. (Saying something is recreational mathematics is NOT an April Fool’s Day joke. Many people actually enjoy mathematics, including me.)

This also is no April Fool’s Day joke: I had a grandson born today at 1:47 pm; He weighed 8 lbs 14 oz.  Print the puzzles or type the factors on this excel file: 10 Factors 2015-03-30

• 444 is a composite number.
• Prime factorization: 444 = 2 x 2 x 3 x 37, which can be written 444 = (2^2) x 3 x 37
• 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 x 2 x 2 = 12. Therefore 444 has exactly 12 factors.
• Factors of 444: 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444
• Factor pairs: 444 = 1 x 444, 2 x 222, 3 x 148, 4 x 111, 6 x 74, or 12 x 37
• Taking the factor pair with the largest square number factor, we get √444 = (√4)(√111) = 2√111 ≈ 21.0713 A Logical Approach to solve a FIND THE FACTORS puzzle: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go. 