Problem
Equal shares with nothing left over means the group size divides 42 exactly, so it is a divisor.
Splitting evenly with nothing left over is the same idea as division with remainder 0, which a 3rd grader meets as 'an unknown-factor' question: students times candies-each equals 42.
3.OA.B.6Make A Systematic ListThe possible numbers of students are exactly the divisors of 42.
Sharing equally with none left over means the 42 candies fall into that many groups of the same size, which is what a divisor describes.
A group size that left anything over would not qualify, so only sizes that divide 42 exactly can be used.
The equal groups and the leftover together account for all 42 candies, so nothing left over is exactly the case where the leftover is zero.
Find every pair of whole numbers that multiplies to 42: 1 and 42, 2 and 21, 3 and 14, 6 and 7. That gives all the divisors of 42.
Listing factor pairs in order makes sure we catch every divisor without missing any or repeating one.
4.OA.B.4Make A Systematic ListThe number of students must be more than 10. From the divisors 1, 2, 3, 6, 7, 14, 21, 42, only 14, 21, and 42 are greater than 10.
Checking each divisor against the 'more than 10' rule filters the full list down to the answers that actually fit the story.
4.OA.B.4Guess And CheckChecking them: 14 x 3, 21 x 2 and 42 x 1 all make 42 with nothing left over.
Multiplying the group size by the candies-each back to 42 proves each split is truly fair with no remainder.
3.OA.B.6Guess And CheckSharing with none left over only works when the number of people is a factor of the total — so just list the factors and pick the ones that fit.