## A Multiplication Based Logic Puzzle

### 104 and Level 3

104 is a composite number. 104 = 1 x 104, 2 x 52, 4 x 26, or 8 x 13. Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104. Prime factorization: 104 = 2 x 2 x 2 x 13, which can also be written 2³ x 13.

104 is never a clue in the FIND THE FACTORS puzzles.

The week’s puzzles and the previous week’s solutions: 10 Factors 2014-04-28

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 and factor 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 table one row at a time as you go:

### 103 and Level 2

103 is a prime number. 103 = 1 x 103. Its only factors are 1 and 103. Prime factorization: none.

How do we know that 103 is a prime number? The square root of 103 is an irrational number approximately equal to 10.15. If 103 were not a prime number, then it would be divisible by at least one prime number less than or equal to 10.15. Since 103 cannot be divided evenly by 2, 3, 5, or 7, we know that 103 is a prime number.

103 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles and last week’s factors: 10 Factors 2014-04-28

### 102 and Level 1

102 is a composite number. 102 = 1 x 102, 2 x 51, 3 x 34, or 6 x 17. Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102. Prime factorization: 102 = 2 x 3 x 17.

102 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles and last week’s solutions: 10 Factors 2014-04-28

### 101 and Level 6

101 is a prime number. 101 = 1 x 101. Its only factors are 1 and 101. Prime factorization: none.

How do we know that 101 is a prime number? The square root of 101 is an irrational number approximately equal to 10.05. If 101 were not a prime number, then it would be divisible by at least one prime number less than or equal to 10.05. Since 101 is not divisible by 2, 3, 5, or 7, it is a prime number.

101 is never a clue in the FIND THE FACTORS puzzles.

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

### 100 and Level 5

100 is a composite number, and it is 10 squared. 100 = 1 x 100, 2 x 50, 4 x 25, 5 x 20, or 10 x 10. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100. Prime factorization: 100 = 2 x 2 x 5 x 5, which can also be written 100 = 2² x 5².

Since √100 = 10, a whole number, 100 is a perfect square.

100 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 (the sum of the first 9 prime numbers).

1³ + 2³ + 3³ + 4³ = 100

Sometimes 100 is a clue in the FIND THE FACTORS puzzles. Even though it has other factors, when it is a clue, the factors are always 10 x 10.

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

### 99 and Level 4

99 is a composite number. 99 = 1 x 99, 3 x 33, or 9 x 11. Factors of 99: 1, 3, 9, 11, 33, 99. Prime factorization: 99 = 3 x 3 x 11, which can also be written 99 = 3² x 11.

Sometimes 99 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we use only 9 x 11 in the puzzles.

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

### 98 and What Do You Do When You Get to the End of a Shoe Lace?

98 is a composite number. 98 = 1 x 98, 2 x 49, or 7 x 14. Factors of 98: 1, 2, 7, 14, 49, 98. Prime factorization: 98 = 2 x 7 x 7, which can also be written 98 = 2 x 7²

98 is never a clue in the FIND THE FACTORS puzzles.

In the past finding the factors for a level 3 puzzles has been like lacing  an entire shoe with only one end of the lace. Today’s puzzle is slightly more difficult because that end of the lace gets cut off in the middle of the puzzle, and the other end of the lace has to be used to find the rest of the factors. Level 3 is meant to be a bridge between the easier levels and the higher leveled puzzles, and those laces get cut off in the higher leveled puzzles all the time. Good luck with this level 3 puzzle! I’m sure you can still find all the factors!

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-21

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 and factor 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 table one row at a time as you go: