Blog #4 Stephen

YAY, FALCONS WON THE GAME!! :) jk.

Anyway. Blog..blog...yes, blog.

Question 1:
What is the prime factorization of 1332?

1332: 148 x 9

2x74x9

2x2x37x3x3

2^2 x 3^2 x 37

Question 2:
What is the gcd and lcm of 240 and 840?

gcd (240, 840)

240: 2x120

2x2x60

2x2x2x30

2x2x2x2x15

2x2x2x2x3x5

240: 2^4 x 3 x 5

840: 3x280

3x2x140

3x2x2x70

3x2x2x2x35

3x2x2x2x5x7

840: 2^3 x 3 x 5 x 7

gcd: 2^3 x 3 x 5 = 120

lcm: 2^4 x 3 x 5 x 7 = 1680

Question 3:
Is 133 prime? What about 103? How did you find out that it is/is not (without looking it up.)

133 is not prime because it is divisible by 7 and 19. 103 is prime because its only factors are 1 and 130.

Question 4:
What is the remainder when 4803925 is divided by 2? What is it when it is divided by 3? By 5? By 13?
How did you figure each of these out?

by 2 = 1

by 3 = 1

by 5 = 0

by 13 = 9

I used the remainder theorem. Divide regularly, then take the integer part and multiply by the divisor. Then subtract that from the original number, and you get the remainder.

Example: Remainder when 13 is divided by 7.

13/7 = 1.857

1 x 7 = 7

13 - 7 = 6

the remainder is 6