28 is a composite number. 28 = 1 x 28, two x 14, or 4 ten 7. Factors of 28: i, 2, 4, 7, 14, 28. Prime number factorization: 28 = ii x 2 x seven, which tin also be written 28 = 2² x vii.

When 28 is a inkling in the FIND THE FACTORS puzzles, the factors will be 4 and 7.

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This snowflake is actually a logic puzzle based on the multiplication table. Because it is a level 5 puzzle, it can be a picayune catchy to solve, and isn't for beginners. If you oasis't solved a Discover the Factors puzzle before, this level ii snowflake puzzle might be a better choice:

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How do you solve a level 5 FIND THE FACTORS one – 12 puzzle? Every bit always the object is to write the numbers 1-12 in the top row and again in the first column and then that those numbers are the factors of the given clues. Use logic, not guessing and checking, to notice its unique solution. Here is how to solve a level 5 puzzle:

Begin past looking for perfect foursquare clues, ane, 25, 49, 64, 81, 100, 121, or 144, considering at that place is but one manner to cistron any of them so that both factors are numbers from i to 12. IF you find one of THOSE perfect foursquare clues, write downward its factors in the corresponding factor row and gene column.

Next locate a row or a column with at least 2 clues. Discover ALL the common factors of that row or cavalcade that will allow you to write only numbers from 1 to 12 in both the factor row and the gene column. If that row or column has more than ane common factor, leave information technology lonely for now. In a level five puzzle there will be at least one row or column that has merely one common factor. When you find such a row or column, write its factors in the corresponding gene cells.

Permit'south use the level 5 puzzle from wk 1 – 2014 every bit an instance. Starting at the top of the puzzle look at all each row to see if it has more than one clue. We discover that there are two rows with ii clues, but in both cases, in that location is more than one possible mutual factor, then we will ignore those rows for now. Starting on the left, look at each column to run across if information technology has more than than one inkling. There are ii columns that have 2 clues, and ane of those columns has 3 possible common factors. If you lot were to approximate which of those factors were correct, yous would have a 67% chance of guessing wrong. Guessing and checking leads to frustration. Use logic and start with the column that has but one possible common cistron, in this instance: i.

2014-01 Level 5 1st step

Now you have at least three factors written downwardly. Next look at ALL the remaining clues in the puzzle and find 1 that can only be factored using one of the factors y'all've written down already just haven't used twice. (Y'all notice that 54 = 9 x 6, and so you lot tin can write ix and six in the appropriate cells.)

One-time during this process, you will discover that ane or more than of the remaining rows or columns that had more than 1 clue take had some of the possible factors eliminated. Logic, or the procedure of emptying, will assistance you know the but mutual factor that will work for those clues in this puzzle. (In last week's puzzle, you may discover that 28 = 4 x seven. That ways that 16 cannot be 4 x 4 because we can't have whatever gene used more than i time in either the cistron row or the gene cavalcade. That means in this particular puzzle sixteen = 8 x two. Since you already establish one eight, it is easy to place this 8 and the 2.)

Go on to look at all the clues and use logic until all (or most all) of the factors are found.

If a row or a cavalcade contains no clues, use logic is determine which number from 1 to 12 (or one to 10) should be written in that location.

While working on these puzzles, occasionally count from 1 to 12 (1 to 10) equally you examine numbers in the factor row and gene column to make sure that a number is written only in one case in either place. Practiced luck!

This week's puzzles are also available in an excel file here, if y'all have a spreadsheet plan on your computer yous tin admission it. If you enable editing in excel, you lot tin can type your answers directly onto the puzzle, and yous can also easily print the puzzles. Here is the solution to the Calendar week 1 – 2014, Level 5 puzzle:

2014-01 Level 5 Answer