• 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.

• 261 is a composite number.
• Prime factorization: 261 = 3 x 3 x 29
• 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 261 has 6 factors.
• Factors of 261: 1, 3, 9, 29, 87, 261
• Factor pairs: 261 = 1 x 261, 3 x 87, 9 x 29
• Taking the factor pair with the largest square number factor, we get √261 = (√9)(√29) = 3√29 ≈ 16.155

This puzzle will look like a multiplication table after you find the factors and then fill in the rest of the table.

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

• 259 is a composite number.
• Prime factorization: 259 = 7 x 37
• 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 259 has 4 factors.
• Factors of 259: 1, 7, 37, 259
• Factor pairs: 259 = 1 x 259 or 7 x 37
• 259 has no square factors that allow its square root to be simplified. √259 ≈ 16.093

Here’s a level 1 Find the Factors puzzle:

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

• 258 is a composite number.
• Prime factorization: 258 = 2 x 3 x 43
• 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 258 has 8 factors.
• Factors of 258: 1, 2, 3, 6, 43, 86, 129, 258
• Factor pairs: 258 = 1 x 258, 2 x 129, 3 x 86, or 6 x 43
• 258 has no square factors that allow its square root to be simplified. √258 ≈ 16.062

Level 6 puzzles aren’t easy. Can you solve this one?

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

• 256 is a composite number.
• Prime factorization: 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, which can be written 256 = 2⁸
• The exponent in the prime factorization is 8. Adding one we get (8 + 1) = 9. Therefore 256 has 9 factors.
• Factors of 256: 1, 2, 4, 8, 16, 32, 64, 128, 256
• Factor pairs: 256 = 1 x 256, 2 x 128, 4 x 64, 8 x 32, or 16 x 16
• 256 is a perfect square. √256 = 16.

((2²)²)² = 256

1 + 3 + 5 + 7 + 9 + 11 + … + 29 + 31 = 256; that’s the sum of the first 16 odd numbers.

Because it is a power of 2, it is impossible to write 256 as the sum of consecutive whole numbers.

ALL of the factors of 256 are powers of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256

NONE of the clues in this level 4 puzzle are powers of 2, but can you still solve it and figure out where the powers of 2 belong in the puzzle?

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

• 255 is a composite number.
• Prime factorization: 255 = 3 x 5 x 17
• 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 255 has 8 factors.
• Factors of 255: 1, 3, 5, 15, 17, 51, 85, 255
• Factor pairs: 255 = 1 x 255, 3 x 85, 5 x 51, or 15 x 17
• 255 has no square factors that allow its square root to be simplified. √255 ≈ 15.969

Here’s a factoring puzzle for you to solve:

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

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.

• 254 is a composite number.
• Prime factorization: 254 = 2 x 127
• 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 254 has 4 factors.
• Factors of 254: 1, 2, 127, 254
• Factor pairs: 254 = 1 x 254 or 2 x 127
• 254 has no square factors that allow its square root to be simplified. √254 ≈ 15.937

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06

• 253 is a composite number.
• Prime factorization: 253 = 11 x 23
• 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 253 has 4 factors.
• Factors of 253: 1, 11, 23, 253
• Factor pairs: 253 = 1 x 253 or 11 x 23
• 253 has no square factors that allow its square root to be simplified. √253 ≈ 15.906

Print the puzzles or type the factors on this excel file: 12 Factors 2014-10-06