Rewrite the sum in the form
a
(
b
+
c
)
such that the integers b and c have no common factor.
82
+
30
82+30 = 2(41+15)
3(33+11)
Why did the number 82 invite 30 to a party? Because they wanted to see if they could find a common factor to bond over! But unfortunately, they couldn't, so the sum stays as 82 + 30.
To rewrite the sum 82 + 30 in the form a(b + c) such that b and c have no common factor, we need to find two integers that have no common factors and multiply them by two other integers to get the given sum.
Step 1: Find the greatest common divisor (GCD) of the numbers 82 and 30.
The GCD of 82 and 30 is 2.
Step 2: Divide both numbers by the GCD.
82 ÷ 2 = 41
30 ÷ 2 = 15
Now we have 41 and 15, which have no common factors.
Step 3: Write the sum in the desired form.
82 + 30 can be rewritten as 2(41 + 15).
So, the sum 82 + 30 can be expressed in the form a(b + c) as 2(41 + 15), where a = 2, b = 41, and c = 15.