Question

gcd (a, b, 16)
b
solve the following
Given gcd (a,b) =24
find
Given gcd (a, b, c) = 12
find
ged (a, b, c, 16)
find gcd (200, 180, 450)
Find gcd (200, 180, 450, 610)
d​

Answer 1

Answer:

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Answer 2

a) gcd(a,b,16) = 8

b) gcd(a,b,c,16) = 4

c) gcd(200,180,450) = 10

d) gcd(200,180,450,610) = 10

Given:

gcd (a,b) = 24

gcd(a,b,c) = 12

To find:

a) gcd(a,b,16)

b) gcd(a,b,c,16)

c) gcd(200,180,450)

d) gcd(200,180,450,610)

Solution:

a) gcd(a,b) = 24

gcd of a,b means greatest common divisor which refers to the product of prime factors that are common to both a and b with the lowest powers equal to 24.

Therefore, gcd(a,b) = 24 can be written as

gcd(a,b) = 24 = 2³ x 3

To find the gcd(a,b,16) we get,

gcd(a,b) = 24 = 2³ x 3

Prime factors of 16 = 2⁴

gcd(a,b,16) = 2³ = 8

The lowest power is 2³. Therefore the gcd(a,b,16) is 8

b) It is given that gcd(a,b,c) = 12

This means that the product of  prime factors that are common to both a  b and c with the lowest powers equals 12

gcd(a,b,c) = 12 = 2² x 3

Then, gcd(a,b,c,16) is given by

Prime factors of 16 = 2⁴

gcd(a,b,c,16) = 2² = 4

The lowest power is 2² therefore the gcd(a,b,c,16) is 4

c) To find the gcd(200,180,450)

Prime factors of 200 = 2³ x 5²

Prime factors of 180 = 2² x 3² x 5

Prime factors of 450 = 2 x 3² x 5²

gcd(200,180,450) = The product of prime factors of lowest powers

                              = 2 x 5

gcd(200,180,450) = 10

Therefore, the gcd(200,180,450) is 10

d) To find the gcd (200, 180, 450, 610)

From c) it is found that gcd(200,180,450) = 10 = 2 x 5

Prime factors of 610 = 2 x 5 x 6

The gcd(200,180,450,610) = 2 x 5 = 10

Therefore, the gcd(200,180,450,610) is 10

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