The House of Representatives has 435 members. If a committee has a prime number of members, and that number is a factor of 435, then how many members can be on the committee?
or 29 or 3
435 = 5 x 3 x 29
5, 3, or 29
To find the number of members that can be on the committee, we need to determine the factors of 435 and check if they are prime numbers.
First, let's find the factors of 435:
1, 3, 5, 15, 29, 87, 145, 435
Next, let's check if each factor is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
Checking the factors:
- 1 is not a prime number because it's less than 2.
- 3 is a prime number because it is only divisible by 1 and 3.
- 5 is a prime number.
- 15 is not a prime number because it is divisible by 3 and 5.
- 29 is a prime number.
- 87 is not a prime number because it is divisible by 3.
- 145 is not a prime number because it is divisible by 5.
- 435 is not a prime number because it is divisible by 3 and 5.
From this analysis, we can see that there are three prime factors of 435: 3, 5, and 29.
Therefore, a committee can have 3, 5, or 29 members.