Factors, multiples, and primes (age 9+)

Question 1

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

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.

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.

Question 2

Sophia has 294 chairs she wants to line up in rows of 6 for the school assembly. Which statement correctly explains whether she can line up all the chairs with no chairs left over?

Accepted Answer

Since 294 ends with an even digit and its digits add to 15, which is divisible by 3, the number is a multiple of 6.

Answer

Because 294 ends with an even digit, it must be a multiple of 6.

Answer

The sum of the digits of 294 is 15, and because 15 is a multiple of 6, the whole number is a multiple of 6.

Answer

Dividing 294 by 6 gives 48 with a remainder of 6, so it is not a multiple of 6.

Question 3

Which two square numbers add together to make 100?

Accepted Answer

64 and 36

Answer

81 and 19

Answer

49 and 51

Answer

25 and 75

Try three questions

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?

Sophia has 294 chairs she wants to line up in rows of 6 for the school assembly. Which statement correctly explains whether she can line up all the chairs with no chairs left over?

Which two square numbers add together to make 100?

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