364 is an easy tetrahedral number to remember because it is one less than the number of days in a year. It is the ridiculous sum total number of all the birds, rings, maids, dancers, and musicians given over the twelve days of Christmas.

One of 364’s factor pairs is also easy to remember: 7 × 52 = 364. There are 7 days in a week and 52 weeks in a year . . . or rather in a year minus one day.

364 is in this cool pattern:

The factoring information for 364 is below the puzzle.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 364 is a composite number.
• Prime factorization: 364 = 2 x 2 x 7 x 13, which can be written 364 = (2^2) x 7 x 13
• 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 364 has exactly 12 factors.
• Factors of 364: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
• Factor pairs: 364 = 1 x 364, 2 x 182, 4 x 91, 7 x 52, 13 x 28, or 14 x 26
• Taking the factor pair with the largest square number factor, we get √364 = (√4)(√91) = 2√91 ≈ 19.079

Every digit of 363 is divisible by 3, so 363 is divisible by 3 and is a composite number. Its factor information is given below the puzzle.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 363 is a composite number.
• Prime factorization: 363 = 3 x 11 x 11, which can be written 363 = 3 x (11^2)
• The exponents in the prime factorization are 1 and 2. Adding one to each and multiplying we get (1 + 1)(2 + 1) = 2 x 3  = 6. Therefore 363 has exactly 6 factors.
• Factors of 363: 1, 3, 11, 33, 121, 363
• Factor pairs: 363 = 1 x 363, 3 x 121, or 11 x 33
• Taking the factor pair with the largest square number factor, we get √363 = (√3)(√121) = 11√3 ≈ 19.053

362 is even so it is a composite number. Its factors are listed below the puzzle.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 362 is a composite number.
• Prime factorization: 362 = 2 x 181
• 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 362 has exactly 4 factors.
• Factors of 362: 1, 2, 181, 362
• Factor pairs: 362 = 1 x 362 or 2 x 181
• 362 has no square factors that allow its square root to be simplified. √362 ≈ 19.026

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.

When 2^359 is divided by 359, the remainder is 2, so 359 is VERY LIKELY a prime number. Scroll down past the puzzle to know for sure.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 359 is a prime number.
• Prime factorization: 359 is prime.
• The exponent of prime number 359 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 359 has exactly 2 factors.
• Factors of 359: 1, 359
• Factor pairs: 359 = 1 x 359
• 359 has no square factors that allow its square root to be simplified. √359 ≈ 18.947

How do we know that 359 is a prime number? If 359 were not a prime number, then it would be divisible by at least one prime number less than or equal to √359 ≈ 18.947. Since 359 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 359 is a prime number.

358 is even and therefore a composite number. Scroll down below the puzzle to see its factors.

Print the puzzles or type the factors on this excel file: 10 Factors 2015-01-19

• 358 is a composite number.
• Prime factorization: 358 = 2 x 179
• 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 358 has exactly 4 factors.
• Factors of 358: 1, 2, 179, 358
• Factor pairs: 358 = 1 x 358 or 2 x 179
• 358 has no square factors that allow its square root to be simplified. √358 ≈ 18.921

356 is even so it is a composite number. Scroll down past the puzzle to see its factors.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-01-12

• 356 is a composite number.
• Prime factorization: 356 = 2 x 2 x 89, which can be written 356 = (2^2) x 89
• 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 356 has exactly 6 factors.
• Factors of 356: 1, 2, 4, 89, 178, 356
• Factor pairs: 356 = 1 x 356, 2 x 178, or 4 x 89
• Taking the factor pair with the largest square number factor, we get √356 = (√4)(√89) = 2√89 ≈ 18.868

Five can evenly divide into numbers when the last digit is 5, so 355 is a composite number. Scroll down past the puzzle to see its factors.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-01-12

• 355 is a composite number.
• Prime factorization: 355 = 5 x 71
• 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 355 has exactly 4 factors.
• Factors of 355: 1, 5, 71, 355
• Factor pairs: 355 = 1 x 355 or 5 x 71
• 355 has no square factors that allow its square root to be simplified. √355 ≈ 18.841

354 is even and thus divisible by 2, so 354 is a composite number. It is also made from three consecutive numbers so it is divisible by 3. Scroll down past the puzzle to see its factors.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-01-12

• 354 is a composite number.
• Prime factorization: 354 = 2 x 3 x 59
• 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 354 has exactly 8 factors.
• Factors of 354: 1, 2, 3, 6, 59, 118, 177, 354
• Factor pairs: 354 = 1 x 354, 2 x 177, 3 x 118, or 6 x 59
• 354 has no square factors that allow its square root to be simplified. √354 ≈ 18.815

When 2^353 is divided by 353, the remainder is 2, so 353 is VERY LIKELY a prime number. Scroll down past the puzzle to know for sure.

Print the puzzles or type the factors on this excel file: 12 Factors 2015-01-12

• 353 is a prime number.
• Prime factorization: 353 is prime.
• The exponent of prime number 353 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 353 has exactly 2 factors.
• Factors of 353: 1, 353
• Factor pairs: 353 = 1 x 353
• 353 has no square factors that allow its square root to be simplified. √353 ≈ 18.788

How do we know that 353 is a prime number? If 353 were not a prime number, then it would be divisible by at least one prime number less than or equal to √353 ≈ 18.788. Since 353 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 353 is a prime number.

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.