Factor Tree

This manipulative allows you to construct factor trees (to the prime factors) for two numbers, and then from the prime factorization, you are asked to identify the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) of the two given numbers.

Create two factor trees

You can choose either of the given numbers (one yellow and one blue). The manipulative opens with the cursor in one of the divisor boxes of the yellow number, but you can click in any of the four boxes, working with either the blue or the yellow number. When you have typed in a divisor of the given number, press ENTER (from the keyboard). If you try to Enter a number that is not a divisor of the given number, nothing happens; you have to correctly identify a factor. The other divisor of the number you have chosen is displayed. When you enter a non-prime divisor of the number, two new divisor boxes appear to allow you to enter further divisors of the given number. When you enter a prime divisor, the prime shows in a circle and you have reached the end of that branch.
Continue until you reach primes on every branch of both the yellow and blue trees.

Factor Trees are movable

If your trees should run together in the workspace (or if one tree runs off the workspace), click and drag either tree.

Identify common prime factors

The two colored regions in the lower part of the workspace are to contain the prime factors of the corresponding colored numbers. The prime factors that belong to both trees (the common prime factors) are to be dragged into the overlapping region (green). When you drag a common prime from either tree into the overlap region, a matching prime is removed from the other tree. Continue until you have all the common prime factors in the common (overlap) region.

Take care of any remaining prime factors

Drag any remaining prime leaves from the yellow tree into the yellow region, and do the same for the blue tree.

The Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) of the given numbers is the product of all the common primes (the factors in the green region). You may enter the GCF in the box at the lower right in any form (as a product of primes or powers of primes, or simply multiplied out).

The Least Common Multiple (LCM)

The Least Common Multiple (LCM) is the smallest number that contains all the prime factors of both trees, hence the product of all the primes in the colored regions (and hence the GCF times the primes in the yellow and the blue regions). Enter the LCM in the other box at the bottom of the workspace.

Check Results and get a New Problem

You need to have a number in both the LCM and GCF boxes to Check. If both numbers are correct, the computer tells you so.
At any point you can press New Problem.