Number Theory Challenge — Putting It Together (Grade 6)
This capstone mixes everything: a single problem may ask you to factor a number, judge whether it's prime, find a GCF or LCM, and reason from several clues at once.
Understanding number theory challenge
The goal isn't a new rule — it's fluency: choosing the right tool (factor pairs, divisibility rules, prime factorization, GCF/LCM) for each step and combining them confidently.
Seeing it in action
Worked example
Two numbers have a GCF of 6 and are both less than 20. One is 12. What could the other be?
The other must be a multiple of 6 but share no larger factor with 12. Multiples of 6 under 20: 6, 12, 18. Check each: GCF(12,12) = 12 (too big — excluded); GCF(12,6) = 6 ✓; GCF(12,18) = 6 ✓.
So the other could be 6 or 18.
A common mistake, and the fix
Accepting any shared factor instead of the greatest one.
12 and 18 share 1, 2, 3 and 6, so their GCF is 6 and 18 works. 12 and 16 are both even, but they share only 1, 2 and 4, so their GCF is 4 and 16 doesn’t work.
Try a few
Smallest number divisible by both 3 and 4?
LCM.
A prime factor of 30 that is also a factor of 20?
GCF of 12 and 30?
12 = 6 × 2 and 30 = 6 × 5, and 2 and 5 share nothing more.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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