There are 435 representatives and 100 senators serving in the united states congress. How many identical groups with the same numbers of representatives and senators could be formed from all of Congress if we want the largest groups possible? How many representatives and senators would be in each group?
GCF(435,100) = 5
So, 5 groups of 87,20
To find the largest possible number of identical groups with the same number of representatives and senators that can be formed from all of Congress, we need to find the greatest common divisor (GCD) of 435 and 100.
The GCD of 435 and 100 is 5.
To calculate the number of groups, we divide the total number of representatives and senators by the GCD:
435 / 5 = 87 groups
To determine the number of representatives and senators in each group, we divide the total number of representatives and senators by the number of groups:
435 / 87 = 5 representatives per group
100 / 87 ≈ 1 senator per group
Therefore, if we want the largest groups possible with the same numbers of representatives and senators, we can form 87 identical groups with 5 representatives and approximately 1 senator in each group.
To find the number of identical groups with the same number of representatives and senators, we need to find the greatest common divisor (GCD) of 435 and 100.
Step 1: Find the GCD
One way to find the GCD is by using the Euclidean algorithm.
Divide 435 by 100: 435 ÷ 100 = 4 with a remainder of 35.
Divide the previous divisor, 100, by the remainder, 35: 100 ÷ 35 = 2 with a remainder of 30.
Repeat this process until the remainder is 0:
35 ÷ 30 = 1 with a remainder of 5.
30 ÷ 5 = 6 with a remainder of 0.
The GCD of 435 and 100 is 5.
Step 2: Divide Congress into Groups
To find the number of groups, divide the total number of representatives and senators by the GCD:
435 ÷ 5 = 87 groups.
Step 3: Determine the number of representatives and senators in each group
To find the number of representatives and senators in each group, divide the total number of representatives and senators by the number of groups:
435 ÷ 87 = 5 representatives and senators in each group.
So, if we want the largest identical groups possible, we can form 87 groups with 5 representatives and 5 senators in each group.