• 295 is a composite number.
• Prime factorization: 295 = 5 x 59
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 295 has exactly 4 factors.
• Factors of 295: 1, 5, 59, 295
• Factor pairs: 295 = 1 x 295 or 5 x 59
• 295 has no square factors that allow its square root to be simplified. √295 ≈ 17.176

These eleven clues could be pretty tricky!

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10

Today’s Puzzle:

Can you fill out this multiplication table that has only eleven clues?

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10

Factors of 294:

• 294 is a composite number.
• Prime factorization: 294 = 2 x 3 x 7 x 7, which can be written 294 = 2 x 3 x (7^2)
• The exponents in the prime factorization are 1, 1 and 2. Adding one to each and multiplying we get (1 + 1)(1 + 1)(2 + 1) = 2 x 2 x 3 = 12. Therefore 294 has exactly 12 factors.
• Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
• Factor pairs: 294 = 1 x 294, 2 x 147, 3 x 98, 6 x 49, 7 x 42, or 14 x 21
• Taking the factor pair with the largest square number factor, we get √294 = (√6)(√49) = 7√6 ≈ 17.146

Sum-Difference Puzzles:

6 has two factor pairs. One of them adds up to 5, and the other one subtracts to 5. Put those factor pairs in the correct boxes to solve the first puzzle.

294 has six factor pairs. Of of those factor pairs adds up to 35, and a different one subtracts to 35. Identify those factor pairs, and you will be able to solve the second puzzle.

The second puzzle is really just the first puzzle in disguise.

 

• 292 is a composite number.
• Prime factorization: 292 = 2 x 2 x 73, which can be written 292 = 2² x 73
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2  = 6. Therefore 292 has exactly 6 factors.
• Factors of 292: 1, 2, 4, 73, 146, 292
• Factor pairs: 292 = 1 x 292, 2 x 146, or 4 x 73
• Taking the factor pair with the largest square number factor, we get √292 = (√4)(√73) = 2√73 ≈ 17.088.

Can you fill out this multiplication table that has only ten clues?

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10

A Logical Approach to FIND THE FACTORS: 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.

• 291 is a composite number.
• Prime factorization: 291 = 3 x 97
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 291 has exactly 4 factors.
• Factors of 291: 1, 3, 97, 291
• Factor pairs: 291 = 1 x 291 or 3 x 97
• 291 has no square factors that allow its square root to be simplified. √291 ≈ 17.059

Can you complete this multiplication table if you’re given just twelve clues?

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10

• 290 is a composite number.
• Prime factorization: 290 = 2 x 5 x 29
• 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 290 has 8 factors.
• Factors of 290: 1, 2, 5, 10, 29, 58, 145, 290
• Factor pairs: 1 x 290, 2 x 145, 5 x 58, or 10 x 29
• 290 has no square factors that allow its square root to be simplified. √290 ≈ 17.029

Print the puzzles or type the factors on this excel file: 10 Factors 2014-11-10