337 What Will Be the Factors of 2015?

2014-12-312020-04-27 / ivasallay / Leave a comment

Since this is my 337th post, I’ll first give some information about the number 337, then I will predict the factors for 2015.

337 is a prime number.
Prime factorization: 337 is prime.
The exponent of prime number 337 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 337 has exactly 2 factors.
Factors of 337: 1, 337
Factor pairs: 337 = 1 x 337
337 has no square factors that allow its square root to be simplified. √337 ≈ 18.358

How do we know that 337 is a prime number? If 337 were not a prime number, then it would be divisible by at least one prime number less than or equal to √337 ≈ 18.358. Since 337 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 337 is a prime number.

Celebrate the New Year by giving this puzzle a try!

WHAT will be the FACTORS of the YEAR 2015?

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

On New Year’s Eve 2013 I predicted that the positive factors for 2014 would be 1, 2, 19, 38, 53, 106,1007, and 2014, and my predictions were 100% accurate!

On this last day of 2014, I boldly announce my predictions for the factors of the year 2015:

The positive factors for 2015 will be 1, 5, 13, 31, 65, 155, 403, and 2015
Some of these factors will occur in pairs: 1 and 2015, 5 and 403, 13 and 155, as well as 31 and 65.
Unfortunately there will be some negative factors in 2015 as well. They will be -1, -5, -13, -31, -65, -155, -403, and -2015.

Whatever life throws your way, I wish you a happy, healthy, and prosperous 2015.

336 and Level 2

2014-12-302021-02-01 / ivasallay / 2 Comments

Today’s Puzzle:

The sixteen clues given in this puzzle are all you need to complete this multiplication table!

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

Factors of 336:

336 is a composite number.
Prime factorization: 336 = 2 x 2 x 2 x 2 x 3 x 7, which can be written 336 = (2^4) x 3 x 7
The exponents in the prime factorization are 4, 1 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1)(1 + 1) = 5 x 2 x 2 = 20. Therefore 336 has exactly 20 factors.
Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
Factor pairs: 336 = 1 x 336, 2 x 168, 3 x 112, 4 x 84, 6 x 56, 7 x 48, 8 x 42, 12 x 28, 14 x 24 or 16 x 21
Taking the factor pair with the largest square number factor, we get √336 = (√16)(√21) = 4√21 ≈ 18.330

Sum-Difference Puzzles:

84 has six factor pairs. One of those factor pairs adds up to 25, and another one subtracts to 25. Can you determine what those factor pairs are to solve the first puzzle below?

336 has ten factor pairs. One of them adds up to 50, and a different one subtracts to 50. 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?

335 and Level 1

2014-12-292020-04-27 / ivasallay / Leave a comment

335 is a composite number.
Prime factorization: 335 = 5 x 67
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 335 has exactly 4 factors.
Factors of 335: 1, 5, 67, 335
Factor pairs: 335 = 1 x 335 or 5 x 67
335 has no square factors that allow its square root to be simplified. √335 ≈ 18.303

If you can multiply, divide and use a little logic, you should easily be able to complete this multiplication table puzzle.

Print the puzzles or type the factors on this excel file: 12 Factors 2014-12-29

334 and Level 6

2014-12-272020-04-27 / ivasallay / Leave a comment

334 is a composite number.
Prime factorization: 334 = 2 x 167
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 334 has exactly 4 factors.
Factors of 334: 1, 2, 167, 334
Factor pairs: 334 = 1 x 334 or 2 x 167
334 has no square factors that allow its square root to be simplified. √334 ≈ 18.276

Solving this Level 6 puzzle can be a little tricky: Is 1 or 2 the common factor for 6 and 8? Is 3 or 6 the common factor for 12 and 30? Is 4 or 8 the common factor for 40 and 16? In each case only one of those choices will make this puzzle work as a multiplication table? Can you figure out what those choices should be? Use logic to find the correct solution, not trial and error.

Print the puzzles or type the factors on this excel file: 10 Factors 2014-12-22

333 and Level 5

2014-12-262020-04-27 / ivasallay / Leave a comment

333 is a composite number.
Prime factorization: 333 = 3 x 3 x 37, which can be written 333 = 3² x 37
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 333 has exactly 6 factors.
Factors of 333: 1, 3, 9, 37, 111, 333
Factor pairs: 333 = 1 x 333, 3 x 111, or 9 x 37
Taking the factor pair with the largest square number factor, we get √333 = (√9)(√37) = 3√37 ≈ 18.248

Can the eleven clues in this puzzle help you to complete this multiplication table?

Print the puzzles or type the factors on this excel file: 10 Factors 2014-12-22

331 and Hockey Sticks

2014-12-242020-04-27 / ivasallay / Leave a comment

331 is a prime number.
Prime factorization: 331 is prime.
The exponent of prime number 331 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 331 has exactly 2 factors.
Factors of 331: 1, 331
Factor pairs: 331 = 1 x 331
331 has no square factors that allow its square root to be simplified. √331 ≈ 18.193

How do we know that 331 is a prime number? If 331 were not a prime number, then it would be divisible by at least one prime number less than or equal to √331 ≈ 18.193. Since 331 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 331 is a prime number.

2014-51 Level 3

Print the puzzles or type the factors on this excel file: 10 Factors 2014-12-22

Today’s puzzle looks like a hockey stick. Hockey sticks remind me not only of the obvious winter sport but also of the Twelve Days of Christmas and Pascal’s triangle.

Dimacs.rutgers.edu explains quite nicely how a hockey stick in Pascal’s triangle can give you the total number of gifts received after one day, two days, three days, and so on. Look at the green and red hockey stick with bold black numbers in this illustration of Pascal’s triangle:

If someone gave you one partridge every day for 12 days, two turtle doves every day for 11 days, three French hens every day for 10 days, etc, etc, and etc, then you would receive 364 gifts. (364 is so easy to remember because it is one less than the number of days in a year.)

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.