My Special Number

My Special Number 63 1 By John Kim

Index • Why I chose the number. Pg: 4 • Three or four connections related to my own world. Pg: 5 • Three, four or more mathematical facts about my number. Pg: 6 • Is my number good for the first move for the Factor Game and the Product Game? Pg: 7 • Is my number odd or even?How many factor pairs does it have? Pg: 8 2

Index • Square #s and dimensions Pg: 9 • Venn Diagram Pg: 10 • The prime Factorization of 63. Pg:11 • Common multiples and factors. Pg:12 • The factor string and relatively prime of 63. Pg:13 • Glossary Pg:14~18 • This is all about my special number Pg:19 • The End Pg:20 3

Why I chose the number 63. • I chose that because my dad was born in 1963 and I love my dad. • I also chose it because for the number 1 to 10, I like 6 best and 3 next. • When you multiply 6 by 3, it is 18. I also like 18 so I also like 63 by a mathematical fact. 4

Three or four connections related to my own world. • My dad was born in 1963. • My mom’s height is 1m 63cm. • There is one building name 63building in Korea which I went many times and it is the tallest building in Korea. • I was born at 6:30am in Nov. 29th 1995. 5

Three, four or more mathematical facts about my number. • 63 is a factor of 126. • 63 is a multiple, divisor of 1,3,7,9 and 21. • 126 is a divisor of 63. • Some multiples of 63 is 126, 189, 252, etc…… • 63 is divisible by 126. • 63 is a deficient number because when you the proper factor, it is less than the number itself. 6

Is my number good for the first move for the Factor Game and the Product Game? • For the factor game, my number doesn’t appear. • For the product game, it would be bad move because the good first move is in the middle, but my special number is at the last line. 7

Is my number odd or even?How many factor pairs does it have? • My number is an Odd Number. • It is not an Even Number. • My number has 5 factor pairs. • Those are 1 63, 3 21 and 7 9. • 1,3,7,9, and 21 is a factor and divisor of 63 and 63 is a multiple and divisible by 1,3,7,9, and 21. 8

The prime Factorization of 63 and the exponents. • 63 3 is 21, 21 3 is 7, and 7 7 is 1, so the prime factorization for 63 is 3 3 7. • The exponents of 63 is 3squared 7. • For the factor tree it is 63 21 3 3 1 7 3 So the prime factorization is 3 3 7. 11

Common multiples and factors. • The common multiples of 63 and 36 is 252 because 63 3 is 21, 21 3 is 7 and 36 3 is 12, 12 3 is 4, 4 2 is 2 ,so 3 3 7 3 3 2 = 252. • The common factors of 63 and 36 is 9 because factors of 63 is 1,3,7,9, and 63 and factors of 36 is 1,2,3,4,6,9,12,18, and 36, so the common factors is 9. 12

The factor string and relatively prime of 63. • For # 63, the factor string is 3 3 7. • 63 and 61 is relatively prime because their greatest common factor is 1. • Also 25 and 63 is relatively prime because their greatest common factor is 1 too. 13

Square #s and Dimensions • 63 is not a square number. • I will just show you the examples of square #. • Square #s are numbers like 5 5 is 25 and 25 is an square number. • For example, 6 6 is 36 and 36 is a square number. • One example of Dimensions, 63: 9

Venn diagram • A Venn diagram looks like a circle or an oval. • You can use a Venn diagram to find common multiples or factors. • If you find common multiples or factors, you put the numbers in an intersection and this is how an intersection looks like: intersection 10

Glossary • Factor: # that fits evenly into another #, example: 4 is a factor of 12. • Divisor: # that divides evenly into another #, example: 5 is a divisor of 15. • Product or multiple: When we multiply 2 or more #s, the answer is product- example: 21=3 7. • Deficient number: Proper factors add up to lessthan the # itself, example: primes: 9, 15, etc.. • Quotient: An answer to a division problem. For example, 12 4 is 3. 3 is a quotient. 14

Glossary • Proper factor: All the factors of a # except the # itself, example: proper factor of 12 is 1,2,3,4,6. NOT 12. • Odd #: A whole # that is not a multiple of 2, example: 1, 3,5,9, etc… • Relatively prime #s: A pair of #s with no common factors except for 1. For example 2 and 3 is a relatively prime # because their GCF is 1. 15

Glossary • Even #: A multiple of 2. When you divide an even # by 2, the remainder is 0. Example: 0,2,4,6,8, etc.. • Remainder: The leftover # when division doesn’t happen evenly. For example, 20 divide by 7 is 2 remainder 6. • Factor pair: Two whole #s that are multiplied to get a product. For example: 4 and 13 is a factor pair of 52 because when you multiply 13 by 4, it is 52. • Exponent: The small raised # that tells you how many times a factor is used. For example, 5 cubed means 5 5 5. 16

Glossary • Venn Diagram: A diagram in which overlapping circles are used to show relationships among sets of objects that have certain contributes. • Prime factorization: A product of prime #s, perhaps with some repetitions, resulting in the desired #. For example, the prime factorization of 30 is 2 3 5. • Dimensions: Rectangle that are the length of its side. 17

Glossary • Common multiple: A multiple that 2 or more #s share. For example, the first few multiples of 5 are 5,10,15,20,25,30,35,35, and 40. Multiples of 7 are 7,14,21,28,35,42, and 49. the common multiples of 5 and 7 is 35. • Common factor: A factor that 2 or more #s share. For example, 5 is a common factor of 15, and 25 because 5 can go into those #s. 18

This is all about My Special Number. 19

The End 20

My Special Number