My special number 60!

1. My special number 60! By Nanako

2. 60…prime or composite? There are two different kinds of numbers. Prime numbers and composite numbers. Prime numbers: A number with exactly 2 factors. Not “a number divisible by only 1 and itself” because one is not prime! It only has one factor! Composite numbers: A number with more than 2 factors. Since 60 has 12 factors, which is more than 2, it is a composite number.

3. 60’s factors 1,2,3,4,5,6,10,12,15,20, 30, 60 These are all of 60’s factors, but 60’s proper factors are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 Factor pairs 60’s factor pairs are: 1 and 60, 2 and 30, 3 and 20, 4 and 15, 5 and 12, 6 and 10. Factor pairs are 2 numbers that are multiplied together to equal a number. For example, I know that I haven’t missed any because I used a factor rainbow to find the factor pairs. When you use a factor rainbow to find factor pairs, it lets you find all the factors and factor pairs of a number without missing anything. x = This means that and are factor pairs of 1 2 3 4 5 6 10 12 15 20 30 60

4. is 60 an abundant, deficient, or perfect number? First of all, this is the definition for abundant, deficient, and perfect numbers. Abundant: A number with proper factors that have a sum greater tan the number itself. Example: 12 is abundant because it’s proper factors add up to 16, which is more than 12…1+2+3+4+6=16 16>12 Deficient: A number with proper factors that have a sum less than the number itself. Example: 15 is deficient because it’s proper factors add up to 9, which is less than 15…1+3+5=9 9<15 Perfect: A number with proper factors that have a sum equal to the number itself. Example: 28 is perfect because it’s proper factors add up to 28, which is exactly the number itself (28). 1+2+4+7+14= 28 28=28 If you add up all of 60’s proper factors, then you get 168. 1+2+3+4+5+6+10+12+15+20+30 = 168. 168>60 This means that 60 is an abundant number.

5. Is 60 even or odd number? 60 is an even number, not an odd number. I know this because even numbers always end in 0,2,4,6,8, and odd numbers end in 1,3,5,7,9. 60 ends in a zero, 60, which means that it is an even number. Every number is either even of odd. After an even number is an odd number, then it is an even number again. Numbers go in a pattern: Even, odd, even, odd, even, odd…Think of it like this. Even odd even odd even odd even odd even

6. Prime factorization of 60 The prime factorization of 60 is 2*2*3*5 or 22*31*51. 22*31*51 is the same as 2 x 2 x 3 x 5, but it is just written in index notation. The prime factorization of a number is the prime numbers that are multiplied together to equal the number itself. To find the prime factorization of a number, you need to make a factor tree. A factor tree helps you find the prime factorization of a number, because you are breaking down all of the factors until they are all prime. As the prime numbers come up, you circle them so you will know what the factorization is. 60 2 * 30 3 * 10 5 * 2 Prime factorization of 60: 2*2*3*5 or 22*31*51

7. Multiples of 60 Multiples of numbers go on forever…so these are just the first 12 multiples of 60. 60,120,180,240,300,360,420,480,540,600,660,720 60 x any number = a multiple of 60. For example, 60*2 = 120, so 120 is a multiple of 60. 60*3 = 180, so 180 is a multiple of 60.

8. Common factors and common multiples A common factor is a factor that 2 or more numbers have in common. For example, when you line up the factors of 60 and 15, you will notice that they have 1,3,5, and 15 in common. Those are the common factors of 60 and 15. 60’s factors: 1,2,3,4,5,6,10,12,15,20,30,60 15’s factors: 1,3,5,15 A common multiple is a multiple that 2 or more numbers have in common. For example, when you line up the multiples (1-600) of 60 and 30, you will notice that they have 60,120,180,240,300,360,420,480,540,and 600 in common. Those are just some of the common multiples of 60 and 30. 60’s multiples (1-600): 60,120,180,240,300,360,420,480,540,600 30’s multiples (1-600): 30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,540,570,600

9. GCF (greatest common factor) and LCM (least common multiple )of 60 and 15 60’s prime factorization: 2*2*3*5 15’s prime factorization: 3*5 Common factors: 3*5 60 15 60 15 20 * 3 3 * 5 5 * 4 2*2 3*5 LCM =2*2*3*5 =4*15 =60 GCF =3*5 =15 2 * 2 One way to find the GCF and LCM of 60 and 15 is to use a Venn diagram. First, though, you need to find the prime factorizations of both numbers. When you do that, you find out that the prime factorization of 60 is 2*2*3*5, and that the prime factorization of 15 is 3*5. Then, line up the prime factorizations of both numbers, and find the common factors. Using that information, make a Venn diagram in which one circle is for 60’s prime factorization, one for 15’s prime factorization, and the circle in the middle for the common factors. In the middle circle put in the common factors (3*5). In 60, only write the 2*2, because the 3*5 is already written in the middle. Since 15 doesn’t have any other factors other than 2*2, just leave it as it is. Lastly, for the GCF and LCM. For the GCF, multiply the numbers in the middle, which is 3*5, so the GCF is 15. For the LCM, you need to multiply all of the numbers in the diagram, so you do 2*2*3*5, which equals 60. The LCM is 60.

10. Another way to find the gcf and lcm of 60 and 15 GCF = 15 LCM = 60 3*5=15 2*2*3*5 = 60 Another way to find the GCF and LCM of 60 and 15 is to make a table like the one above. In the first 2 columns, write 60 and 15, which is the 2 numbers that you are finding the GCF and LCM of. In the 3rd and 4th columns, write GCF and LCM. Now, starting with 60, write 60’s prime factorization (2*2*3*5) in the next 4 columns. Next, we are going to write the prime factorization of 15 (3*5) in the next row, but since 3*5 is already written once in 60’s prime factorization, just write it underneath it. Now, to find the GCF, take the factors that 60 and 15 have in common (a factor that is in both number’s prime factorization) and multiply those numbers. So you would do 3*5 which equals 15. The GCF of 60 and 15 is 15. Lastly, for the LCM, multiply all of the factors of both 60 and 15. Make sure you only multiply the common factors (3*5) once. So you would do 2*2*3*5 which equals 60, so the LCM of 60 and 15 is 60.

11. Gcf and lcm of 60, 15, and 56 60 15 60 15 56 3 * 5 3*5 2 * 30 7 * 8 Prime factorization of: 60: 2*2*3*5 15: 3*5 56: 2*2*2*7 2 * 15 4 * 2 2*7 3 * 5 2 * 2 2*7 56 To find the GCF and LCM of 60, 15, and 6 (3 numbers), first, you need to find the prime factorization of all the numbers. 60 = 2*2*3*5, 15 = 3*5, and 56 = 2*2*2*7. Next, you need to find what factors they have in common. For example, 60 and 56 have 2*2 in common, and 60 and 15 have 3*5 in common. Now, you will need to put the numbers into the Venn diagram. The numbers that 60 and 56 have in common go in the circle in between the circle for 60 and 56, and the circle between 60 an d 15 is the circle for the factors that they have in common, etc. Once you have put the numbers in, to find the GCF, you multiply the numbers in the very middle of the diagram, but in this case, there is nothing in the middle, which means that the GCF is 1. Lastly, the LCM is all of the numbers in the diagram, so 2*2*3*5*7*7 = 2940. The GCF is 1, and the LCM is 2940.

12. 60 can be the gcf for 300 and 360! 300 Prime factorization of: 300:2*2*3*5*5 360:2*2*2*3*3*5 300 360 3 * 100 2 * 50 2*2*3*5 2*3 5 5 * 10 5 * 2 360 6 * 60 GCF = 2*2*3*5 = 4*15 = 60 2 * 3 * 2 * 30 3 * 10 5 * 2

13. Picture URL’S: http://www.colchesterhospital.nhs.uk/images/NHS%2060%20mosaic.jpg http://rwridley.files.wordpress.com/2009/09/60.png http://www.steinardanielsen.com/wp-content/uploads/2010/08/hello_my-urlis.jpg http://math.phillipmartin.info/math_prime_composite.gif