Question

There are 100 members in the U.S senate. There are 435 members in the U.S house of representatives. If the total number of U.S senators divisible by 2,3,4,5,6,9, or 10?

Answer 1

Answer:

• 100 is divisible by 2, 4, 5, or 10
• 435 is divisible by 3 or 5
• 535 is divisible by 5

Step-by-step explanation:

A number is divisible by 2 if its units digit is even. {0, 2, 4, 6, 8}

"Casting out 9s" is the process of summing digits, repeatedly, until a number 9 or less is obtained. For 435, that process results in ...

  4 + 3 + 5 = 12; 1 + 2 = 3

A number is divisible by 3 if the result of casting out 9s is divisible by 3. {3, 6, 9}

A number is divisible by 4 if its last two digits are divisible by 4.

A number is divisible by 5 if it ends in 0 or 5, and is divisible by 10 if it ends in 0.

A number is divisible by 6 if it is both even and divisible by 3.

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The number 100 is divisible by 2, 4, 5, and 10.

The number 435 has a sum of digits of 3, so is divisible by 3 and 5.

The sum of these numbers, the total number of members of Congress, 535, is divisible by 5 only.

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The other factor of 435 is 29, a prime; the other factor of 535 is 107, a prime.