Factors, multiples, and primes (age 9+)

Question 1

Jaden collected 264 marbles and wants to arrange them into equal groups of 6. Which statement correctly explains whether 264 can be divided evenly by 6?

Accepted Answer

264 is even and the sum of its digits (2+6+4 = 12) is divisible by 3, so it is divisible by both 2 and 3, therefore it is a multiple of 6.

Answer

Since 264 ends with a 4, and numbers ending with 4 are always multiples of 6.

Answer

Because 264 ÷ 3 = 88, it must also be a multiple of 6.

Answer

Dividing 264 by 6 gives 44 remainder 2, so it is not a multiple of 6.

Question 2

A baker is filling two square‑shaped cookie trays. Each tray must contain a perfect‑square number of cookies, and the total number of cookies in both trays is exactly 100. Which two tray capacities could she use?

Accepted Answer

36 cookies and 64 cookies

Answer

16 cookies and 84 cookies

Answer

25 cookies and 75 cookies

Answer

49 cookies and 51 cookies

Question 3

Maya has 210 beads and wants to put the same number of beads in each of several bags, with exactly 6 beads per bag. Which statement correctly explains whether she can do this without any beads left over?

Accepted Answer

The number 210 is even, and the sum of its digits 2 + 1 + 0 = 3 is a multiple of 3; therefore 210 is a multiple of 6 and Maya can fill the bags.

Answer

The digits of 210 add to 3, a multiple of 3, so 210 must be a multiple of 6, letting Maya fill the bags.

Answer

Because 210 ends in 0, it is a multiple of 6, so Maya can fill the bags.

Answer

Since 210 is an even number, it is automatically a multiple of 6, so Maya can fill the bags.

Try three questions

Jaden collected 264 marbles and wants to arrange them into equal groups of 6. Which statement correctly explains whether 264 can be divided evenly by 6?

A baker is filling two square‑shaped cookie trays. Each tray must contain a perfect‑square number of cookies, and the total number of cookies in both trays is exactly 100. Which two tray capacities could she use?

Maya has 210 beads and wants to put the same number of beads in each of several bags, with exactly 6 beads per bag. Which statement correctly explains whether she can do this without any beads left over?

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