Prime factorization

209 and Level 3

/ ivasallay / Leave a comment

2-0+9=11 so 209 is divisible by 11.

  • 209 is a composite number.
  • Prime factorization: 209 = 11 x 19
  • 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 209 has exactly 4 factors.
  • Factors of 209: 1, 11, 19, 209
  • Factor pairs: 209 = 1 x 209 or 11 x 19
  • 209 has no square factors that allow its square root to be simplified. √209 ≈ 14.456832

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 2014-33 Level 3

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

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.

2014-33 Level 3 Factors

208 and Level 2

/ ivasallay / Leave a comment

  • 208 is a composite number.
  • Prime factorization: 208 = 2 x 2 x 2 x 2 x 13, which can be written 208 = 2⁴ x 13
  • 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 208 has exactly 10 factors.
  • Factors of 208: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
  • Factor pairs: 208 = 1 x 208, 2 x 104, 4 x 52, 8 x 26, or 13 x 16
  • Taking the factor pair with the largest square number factor, we get √208 = (√16)(√13) = 4√13 ≈ 14.422205

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 2014-33 Level 2

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

2014-33 Level 2 Factors

207 and Level 1

/ ivasallay / Leave a comment

  • 207 is a composite number.
  • Prime factorization: 207 = 3 x 3 x 23, which can be written 207 = 3² x 23
  • 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 207 has exactly 6 factors.
  • Factors of 207: 1, 3, 9, 23, 69, 207
  • Factor pairs: 207 = 1 x 207, 3 x 69, or 9 x 23
  • Taking the factor pair with the largest square number factor, we get √207 = (√9)(√23) = 3√23 ≈ 14.38749

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 2014-33 Level 1

Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-08-18

2014-33 Level 1 Factors

206 and Level 6

/ ivasallay / Leave a comment

  • 206 is a composite number.
  • Prime factorization: 206 = 2 x 103
  • 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 206 has exactly 4 factors.
  • Factors of 206: 1, 2, 103, 206
  • Factor pairs: 206 = 1 x 206 or 2 x 103
  • 206 has no square factors that allow its square root to be simplified. √206 ≈ 14.35270009

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 2014-32 Level 6

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 6 Logic

205 and Level 5

/ ivasallay / Leave a comment

  • 205 is a composite number.
  • Prime factorization: 205 = 5 x 41
  • 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 205 has exactly 4 factors.
  • Factors of 205: 1, 5, 41, 205
  • Factor pairs: 205 = 1 x 205 or 5 x 41
  • 205 has no square factors that allow its square root to be simplified. √205 ≈ 14.317821

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2014-32 Level 5

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 5 Logic

204 and Level 4

/ ivasallay / Leave a comment

  • 204 is a composite number.
  • Prime factorization: 204 = 2 × 2 × 3 × 17, which can be written 204 = 2² × 3 × 17
  • 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 204 has exactly 12 factors.
  • Factors of 204: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
  • Factor pairs: 204 = 1 x 204, 2 x 102, 3 x 68, 4 x 51, 6 x 34, or 12 x 17
  • Taking the factor pair with the largest square number factor, we get √204 = (√4)(√51) = 2√51 ≈ 14.2828568570856999959987996

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 2014-32 Level 4

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 4 Logic

203 and Level 3

/ ivasallay / 2 Comments

  • 203 is a composite number.
  • Prime factorization: 203 = 7 x 29
  • 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 203 has exactly 4 factors.
  • Factors of 203: 1, 7, 29, 203
  • Factor pairs: 203 = 1 x 203 or 7 x 29
  • 203 has no square factors that allow its square root to be simplified. √203 ≈ 14.2478068

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2014-32 Level 3

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

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.

2014-32 Level 3 Factors

202 and Level 2

/ ivasallay / Leave a comment

  • 202 is a composite number.
  • Prime factorization: 202 = 2 x 101
  • 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 202 has exactly 4 factors.
  • Factors of 202: 1, 2, 101, 202
  • Factor pairs: 202 = 1 x 202 or 2 x 101
  • 202 has no square factors that allow its square root to be simplified. √202 ≈ 14.2126704

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2014-32 Level 2

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 2 Factors

201 World Elephant Day

/ ivasallay / 3 Comments

Why Is There a World Elephant Day Each Year?

Today is World Elephant Day, and today, like every other day in recent history, about 100 elephants will be killed by poachers.

Elephant Multiplication Rhyme

I’ve written the multiplication rhyme above not only to help children remember 11 x 11 = 121, but also to teach them never to buy ivory and to work to protect elephant families. Elephants are magnificent for many reasons, and they live in family units just like we do.

Picture your family sitting down with a few other families for dinner in an outdoor cafe when suddenly all the adults are fired upon and killed by thieves. Your orphaned children witness as the thieves remove rings from your fingers and other valuables from your now dead body.

That is what happens to scores of elephant families EVERYDAY as poachers selfishly remove ivory from the elephants they massacre.

Imagine a world with NO elephants. That day is in our future unless we do all we can to change the present.

Please, take a few minutes to check out some of these blogs that are written by people who truly love elephants:

runnergirlrobin world-elephant-day-a-cause-near-dear-to-my-heart

saltwaterspeculation world-elephant-day

world-elephant-day-here-are-some-interesting-facts

kenyan-elephant-activist-wants-an-ivory-arrest

go-grey-for-elephants

remembering-our-elephants

celebrate-world-elephant-day

mama-and-baby-elephant

Factors of 201:

2 + 0 + 1 = 3, so 201 is divisible by 3.

  • 201 is a composite number.
  • Prime factorization: 201 = 3 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 201 has exactly 4 factors.
  • Factors of 201: 1, 3, 67, 201
  • Factor pairs: 201 = 1 x 201 or 3 x 67
  • 201 has no square factors that allow its square root to be simplified. √201 ≈ 14.1774

More About the Number 201:

When 201 and 102 are squared, it is almost like they are looking in a mirror at each other:

201² = 40401, and
102² = 10404.

How uncommon is it that the square of a number and the square of the number made by reversing its digits are reverses of each other? This chart lists the 50 numbers that are the ONLY numbers less than 10000 that can make that claim.

Numbers-and-Their-Reverses-and-Squares.jpg (750×353)

200 and Level 1

/ ivasallay / 1 Comment
200 is a composite number.
Factor pairs: 200 = 1 x 200, 2 x 100, 4 x 50, 5 x 40, 8 x 25, or 10 x 20
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Prime factorization: 200 = 2 x 2 x 2 x 5 x 5, which can be written 200 = (2^3) x (5^2)

200 is the smallest positive number that cannot be turned into a prime number by changing ONE of its digits to a different digit. If you can remember that little fact, if should help you to remember that ALL the numbers from 200 to 210 are composite numbers.

2014-32 Level 1

Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-08-11

2014-32 Level 1 Factors