• 273 is a composite number.
• Prime factorization: 273 = 3 × 7 × 13
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2= 8. Therefore 273 has exactly 8 factors.
• Factors of 273: 1, 3, 7, 13, 21, 39, 91, 273
• Factor pairs: 273 = 1 × 273, 3 × 91, 7 × 39, or 13 × 21
• 273 has no square factors that allow its square root to be simplified. √273 ≈ 16.523

Find the Factors is now one of  many  interesting mathematical resources that can be found on Solvemymaths!

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

• 272 is a composite number.
• Prime factorization: 272 = 2 x 2 x 2 x 2 x 17, which can be written (2^4) x 17
• The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 x 2 = 10. Therefore 272 has 10 factors.
• Factors of 272: 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
• Factor pairs: 272 = 1 x 272, 2 x 136, 4 x 68, 8 x 34, or 16 x 17
• Taking the factor pair with the largest square number factor, we get √272 = (√16)(√17) = 4√17 ≈ 16.492

Give this Level 4 puzzle a try!

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

Today’s Puzzle:

Can you solve this level 2 puzzle?

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

Factors of 270:

• 270 is a composite number.
• Prime factorization: 270 = 2 x 3 x 3 x 3 x 5, which can be written 2 x (3^3) x 5
• The exponents in the prime factorization are 1, 3, and 1. Adding one to each and multiplying we get (1 + 1)(3 + 1)(1 + 1) = 2 x 4 x 2 = 16. Therefore 270 has 16 factors.
• Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
• Factor pairs: 270 = 1 x 270, 2 x 135, 3 x 90, 5 x 54, 6 x 45, 9 x 30, 10 x 27, or 15 x 18
• Taking the factor pair with the largest square number factor, we get √270 = (√9)(√30) = 3√30 ≈ 16.432

Sum-Difference Puzzles:

30 has four factor pairs. One of those factor pairs adds up to 13, and another subtracts to 13. Can you find those factor pairs to solve the first puzzle below?

270 has eight factor pairs. One of them adds up to 39, and a different one subtracts to 39. If you can identify those factor pairs, then you can solve the second puzzle!

The second puzzle is really just the first puzzle in disguise. Why would I say that?

Factors for Today’s Puzzle:

 

• 268 is a composite number.
• Prime factorization: 268 = 2 x 2 x 67, which can be written (2^2) x 67
• 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 268 has 6 factors.
• Factors of 268: 1, 2, 4, 67, 134, 268
• Factor pairs: 268 = 1 x 268, 2 x 134, or 4 x 67
• Taking the factor pair with the largest square number factor, we get √268 = (√4)(√67) = 2√67 ≈ 16.371.

Here is today’s puzzle:

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-20

• 267 is a composite number.
• Prime factorization: 267 = 3 x 89
• 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 267 has 4 factors.
• Factors of 267: 1, 3, 89, 267
• Factor pairs: 267 = 1 x 267 or 3 x 89
• 267 has no square factors that allow its square root to be simplified. √267 ≈ 16.3401

Can you solve this level 6 puzzle? Possible steps to logically arrive at the solution are given at the end of the post.

Print the puzzles or type the factors on this excel file: 10 Factors 2014-10-13

• 265 is a composite number.
• Prime factorization: 265 = 5 x 53
• 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 265 has 4 factors.
• Factors of 265: 1, 5, 53, 265
• Factor pairs: 265 = 1 x 265 or 5 x 53
• 265 has no square factors that allow its square root to be simplified. √265 ≈ 16.279

Here is today’s puzzle:

Print the puzzles or type the factors on this excel file: 10 Factors 2014-10-13

• 264 is a composite number.
• Prime factorization: 264 = 2 x 2 x 2 x 3 x 11, which can be written (2^3) x 3 x 11
• The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16. Therefore 264 has 16 factors.
• Factors of 264: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
• Factor pairs: 264 = 1 x 264, 2 x 132, 3 x 88, 4 x 66, 6 x 44, 8 x 33, 11 x 24, or 12 x 22
• Taking the factor pair with the largest square number factor, we get √264 = (√4)(√66) = 2√66 ≈ 16.248

That’s a lot of factors. Finding the factors for this puzzle will be much easier:

Print the puzzles or type the factors on this excel file: 10 Factors 2014-10-13

• 262 is a composite number.
• Prime factorization: 262 = 2 x 131
• 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 262 has 4 factors.
• Factors of 262: 1, 2, 131, 262
• Factor pairs: 262 = 1 x 262 or 2 x 131
• 262 has no square factors that allow its square root to be simplified. √262 ≈ 16.186

Can you solve this factoring puzzle?

Print the puzzles or type the factors on this excel file: 10 Factors 2014-10-13

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.