Question

You have 33 marbles besides one group of 33 marbles is it possible to divide the marbles into groups with the same number of marbles with no marbles left over

Answer 1

Answer:

• Yes, you can divide the 33 marbles into groups of 1, 3, or 11 with the same number of marbles and no marbles left over.

Explanation:

The question is whether a group of 33 marbles can be divided into groups with the same number of marbles with no marbles left, in addition to the possibility of one group of the 33 marbles.

You can answer that question by finding the prime factorization of the number 33.

• 33 = 3 × 11

That means that 33 is divisible by 1, 3, 11, and 33.

Then, obviously one way to divide 33 marbles is 1 group of 33, so besides it you can divide them into these groups:

• 3 groups of 11 marbles, since 3 × 11 = 33,

• 11 groups of 3 marbles, since 11 × 3 = 33, and

• 33 groups of 1 marble, because 33 × 1 = 33

Hence, you have shown that, besides one group of 33 marbles, you can divide the 33 marbles into groups of 1, 3, or 11 with the same number of marbles and no marbles left over.