The prime factorization of 360 can be written in the form
(a^m)(b^n)(c^r). What is the valye of a+b+c-mnr
go ahead, express 360 in that form.
360 = 2* 180
= 2*2*90
= 2*2*2*45
= 2*2*2*3*3*5
= 2^3 * 3^2 * 5^1
so , what do you think ?
You are missing the main point, I did not say that 5 was the answer.
First of all, you have to agree that
2^3 * 3^2 * 5^1 = 360
now match (a^m)(b^n)(c^r) with 2^3 * 3^2 * 5^1
clearly:
a = 2
b = 3
c = 5
m = 3
n = 2
r = 1
then a+b+c-mnr
= 2+3+5 - 3(2)(1)
= 10 - 6
= 4
5 is not one of the choices.
To find the prime factorization of 360, we need to express it as a product of prime numbers.
First, let's divide 360 by the smallest prime number, 2. The result is 180 (360 ÷ 2 = 180).
Again, divide 180 by 2: 180 ÷ 2 = 90.
Continue dividing by 2 until we can't divide evenly anymore: 90 ÷ 2 = 45.
Now, we move on to the next smallest prime number, which is 3. Divide 45 by 3: 45 ÷ 3 = 15.
Divide 15 by 3: 15 ÷ 3 = 5.
Since 5 is a prime number, we can stop here.
The prime factorization of 360 is: 2² × 3² × 5.
So a = 2, m = 2, b = 3, n = 2, and c = 5, r = 1 (assuming the exponents are non-zero).
Now we can substitute these values into the expression a + b + c - mnr:
a + b + c - mnr = 2 + 3 + 5 - (2 × 2 × 1) = 2 + 3 + 5 - 4 = 6 + 5 - 4 = 11 - 4 = 7.
Therefore, the value of a + b + c - mnr is 7.