Foundational Math Mechanics

Grade 6 Unit 1 Foundations

Explore GCF & LCM Venn diagram wheels, prime factorization trees, and essential factor puzzles to master the early year benchmarks.

Venn Wheels GCF & LCM Prime Factor Trees Factor Puzzles

Factors, GCF, and Prime Numbers

GCF and LCM are foundational properties of integers. Review these prime tree guidelines and Venn diagram overlaps before starting your review checkpoints.

📈 Prime vs. Composite

A prime number has exactly two factors: 1 and itself (e.g. 2, 3, 5, 7). A composite number has more than two factors (e.g. 4, 6, 8, 9).

Números Primos: Tienen solo dos factores (1 y sí mismo). Compuestos tienen más.

Primes: 2, 3, 5, 7, 11, 13...

⚖️ Greatest Common Factor

The GCF is the largest number that divides evenly into two or more integers. Find it by identifying overlapping prime factors in a Venn diagram.

Máximo Común Divisor (MCD): El número mayor que divide exactamente a dos o más números.

GCF = product of common primes

📊 Least Common Multiple

The LCM is the smallest multiple shared by two integers. Compute it by multiplying the unique outer prime factors by the common inner ones.

Mínimo Común Múltiplo (mcm): El múltiplo más pequeño que comparten dos números.

LCM = GCF × unique outer primes

Interactive GCF & LCM Venn Wheel

Input two integers, and watch the Venn diagram programmatically draw their overlapping prime factors to calculate the GCF and LCM in real time!

INTERACTIVE VENN DIAGRAM WHEELS

Venn Parameters

Value A:

Value B:

Calculations Scorecard

Common Prime Factors:2, 3

GCF ($2 \times 3$):6

LCM ($3 \times 6 \times 4$):72

Prime Factorization Trees

Select a composite integer to watch the tree programmatically branch out into prime components, representing factors as prime base exponents live!

INTERACTIVE PRIMES TREE DRAW

Tree Parameters

Select Composite Number:

Prime Decompositions

24 = 2³ × 3

GRADE: -- / 100

0 / 4 Answered

1 GCF Calculations

What is the **Greatest Common Factor** of 24 and 36?

A) 6

B) 8

C) 12

D) 18

2 LCM Calculations

What is the **Least Common Multiple** of 8 and 12?

A) 12

B) 24

C) 36

D) 48

3 Prime Factorization

Which of the following represents the correct **prime factorization** of 40?

A) $2 × 2 × 10$

B) $2² × 5$

C) $2³ × 5$

D) $2 × 20$

4 Prime vs Composite Identifier

Which of the following sets contains **ONLY prime numbers**?

A) {2, 3, 5, 7, 11}

B) {1, 2, 3, 4, 5}

C) {2, 3, 5, 9, 11}

D) {3, 5, 7, 9, 13}

🏆 Foundations Certified Master!

Unit 1 foundations Master

100%

Outstanding! You have mastered GCF, LCM, prime factorizations, and factor puzzle benchmarks.