Greatest Common Factor
Factor Fleet
Load blue and gold crystals into the largest possible fleet of identical pods. Try different pod counts, check the leftovers, and launch when every crystal is packed. Each launch shows how to use the greatest common factor to write a sum as a product.
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How to play Factor Fleet
- 1
Read the supply
Look at the total of each color. Every pod must get the same number of blue crystals as every other pod, and the same number of gold crystals as every other pod.
- 2
Choose how many pods to load
Select a pod count. Look at the quantities in each pod and check both Left over counters. A count works only when both counters are zero.
- 3
Launch the largest fleet
Select Launch when you think you have the greatest count that divides both totals. If the fleet is too small or there are leftovers, change the count and retry.
- 4
Read the equation and keep flying
Read the equation for the successful split, then select Next shipment. After five launches, select Play again for a fresh mission.
Key Features
A live cargo bay
Choose from 1 to 12 pods. Each pod shows how many blue and gold crystals it gets, and the Left over counters show what stays behind.
Two kinds of feedback
Launch tells you when a split leaves crystals behind or when the crystals fit but a larger fleet is possible. Change the pod count and try again on the same shipment.
Factored sums
After a successful launch, the equation connects the total of each color to the number of pods and the load in each pod.
Five shipments per mission
Earn 100 points per launch, with a bonus for consecutive launches without misses. Play again gives you a new set of crystal totals.
What is Factor Fleet?
Factor Fleet is a sixth-grade math game about finding the greatest common factor (GCF) by building equal groups. With 36 blue crystals and 8 gold crystals, 2 pods can take 18 blue and 4 gold each. Four pods can take 9 blue and 2 gold each, with nothing left behind. Four is the largest fleet that works, so the launch shows 36 + 8 = 4 × (9 + 2).
Why play Factor Fleet?
- 1
Test a factor of both totals
A pod count must divide each color separately. Adding the colors and dividing the combined total can hide leftovers of one color.
- 2
Compare two common factors
Try 2 pods and 4 pods with 36 and 8. Both counts work, but the mission asks for the greater one.
- 3
Distinguish the groups from their contents
The multiplier counts pods. The numbers inside the parentheses count blue and gold crystals inside one pod.
- 4
Practice several kinds of pairs
Some shipments have several common factors, some have one total that divides the other, and some can only fit in a single pod.
Frequently Asked Questions
What is a common factor?
A common factor divides both numbers evenly. In the cargo bay, it is a pod count that leaves zero blue and zero gold crystals behind.
Why did a split with zero leftovers fail?
You found a common factor. A larger count still divides both totals, and Launch needs the greatest common factor.
Can one pod be the answer?
Yes. When the two numbers share only the factor 1, one pod holds both supplies and is the largest fleet that works.
Do the blue and gold loads have to match each other?
Each color has to match across all pods. One pod can hold 9 blue and 2 gold if every other pod holds those same two amounts.
Can I play with a keyboard?
Yes. Tab to a pod count or a control, then press Enter or Space to use it.
