StackCalc Prime Factor Studio 29 Blocks with Snapfinity Box

Prime Factor Towers with Snapfinity Storage Box

Prime Factor Studio & Factor Towers

Q: How does stacking prime blocks physically multiply numbers?

Every prime block has a visible height equal to 42.0 * log10(p) mm. Because logarithms convert multiplication into addition (log(a * b) = log(a) + log(b)), stacking a [2] block (12.64mm) and a [3] block (20.04mm) creates a total visible height of 32.68mm—which matches Composite Factor Tower [6] with 0.000mm error.

Q: How does the kit prove the Fundamental Theorem of Arithmetic?

The Fundamental Theorem states that every integer greater than 1 has a unique prime factorization. Students discover this physically: whether building 36 from 4 x 9 or 6 x 6, both factor trees decompose into the exact same prime blocks: two [2]s and two [3]s (2^2 x 3^2 = 36). No other combination of prime blocks can ever match that height.

Q: How does the set demonstrate Greatest Common Factor (GCF) and Least Common Multiple (LCM)?

To find GCF(12, 18), students build the tower for 12 ([2]+[2]+[3]) and 18 ([2]+[3]+[3]). The identical overlapping blocks shared by both towers are one [2] and one [3], giving GCF = 2 x 3 = 6. For LCM, students build the shortest combined tower containing all factors of both, reaching height 36.

PEDAGOGICAL STANDARD • Concrete Proof of Fundamental Theorem of Arithmetic ✓ 42mm Gridfinity Compliant

$46.00 ✓ Free US Shipping • In Stock

The world's first physical logarithmic manipulative for prime factorization, prime vs. composite numbers, and early number theory. Contains 29 proportional stacking prime factor blocks (powers of 2, 3, 5, 7, and higher prime markers) paired with a 3×1×13U Snapfinity Gridfinity box with integrated prime power lid sockets. Stacking prime blocks physically multiplies them, matching composite factor heights with 0.000mm error.

✓ Physical Proof of $a \times b = b \times a$: Stacking [2] then [5] reaches exactly the same height as [5] then [2] (both reach 42.00mm, representing product 10), physically proving the commutative property of multiplication.

✓ Additive Logarithmic Geometry: Each block's visible height is $42.0 \times \log_{10}(p)\text{ mm}$. Because $\log(ab) = \log(a) + \log(b)$, physical tower height directly measures the arithmetic product.

✓ Fundamental Theorem of Arithmetic: Any composite number decomposes into a single unique set of prime blocks (e.g. $36 = 2^2 \times 3^2$), eliminating abstract factoring confusion.

✓ Prime Power Storage Lid: Docking sockets for $2^6, 3^4, 5^2, 7^2, 11, 13, 17, 19, 23$ and an authentic HP-32 hardware replica button badge stamped [FACT].

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± ±0.05mm Calibrated • Non-Toxic Biopolymer

✓ Anti-Heartbreak $2.49 Part Refills

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The Video Showcase: Animated Step-by-Step Lessons & Kinematics

Experience logarithmic factor stacking, the Fundamental Theorem of Arithmetic, and LCM/GCD Venn towers directly from our curriculum guide.

1. CURRICULUM LESSON 01

Fundamental Theorem of Arithmetic

Step-by-step physical multiplication: stacking logarithmic prime blocks [2] and [3] to match the exact height of composite factor tower [6].

CCSS 6.NS.B.4 2 × 3 = 6 Flush

2. CURRICULUM LESSON 02

LCM & GCD Venn Stacking

Decomposing 12 and 18 into prime towers. Extracting shared intersection blocks for GCD (6) and union blocks for LCM (36).

CCSS 6.NS.B.4 GCD=6 • LCM=36

3. CURRICULUM LESSON 03

Unique Prime Factorization: 36 = 2² × 3²

Building 36 along two distinct branching paths (4 × 9 vs. 6 × 6). Both towers level to the exact same 36.00mm summit (0.000mm error), proving factorization is unique and commutative.

CCSS 4.OA.B.4 • 6.NS.B.4 Summit = 36 Flush

Archival Reference & Video QR Card (135×90mm)

Included inside every box. Scan Side B to jump straight to this animated video lesson portal or inspect Side A for replacement part dimensions.

View Front (Side A) View Back (QR Side B) Print Duplex Sheet

MATHEMATICAL PROOF // LOGARITHMIC TOWER ALIGNMENT ● 0.000 MM ERROR • THE FUNDAMENTAL THEOREM OF ARITHMETIC

In middle school arithmetic, students are taught to draw "factor trees" on paper. While tree diagrams show branching, they fail to convey magnitude—a prime 2 looks the same size as a composite 24. Prime Factor Studio grounds abstract prime factorization in physical spatial geometry:

Target Number $N$	Prime Blocks Stacked	Visible Height $\sum h_{\text{vis}}$	Desk Stacking Top $Z_{\text{top}}$	Target Height $Z_{\text{target}}$	Alignment Delta
$N = 2$	`[2]`	12.64 mm	14.49 mm	14.49 mm	0.000 mm (Exact)
$N = 4$	`[2]` + `[2]`	25.29 mm	27.14 mm	27.14 mm	0.000 mm (Exact)
$N = 6$	`[2]` + `[3]`	32.68 mm	34.53 mm	34.53 mm	0.000 mm (Exact)
$N = 10$	`[2]` + `[5]`	42.00 mm	43.85 mm	43.85 mm	0.000 mm (Exact)
$N = 20$	`[2]` + `[2]` + `[5]`	54.64 mm	56.49 mm	56.49 mm	0.000 mm (Exact)
$N = 50$	`[2]` + `[5]` + `[5]`	71.36 mm	73.21 mm	73.21 mm	0.000 mm (Exact)
$N = 100$	`[2]`² + `[5]`²	84.00 mm	85.85 mm	85.85 mm	0.000 mm (Exact)

// HARDWARE INVENTORY (29 BLOCKS)

12× [2] Factor Blocks: Teal / Blue ($h_{\text{vis}} = 12.64\text{ mm}$)
8× [3] Factor Blocks: Amber / Green ($h_{\text{vis}} = 20.04\text{ mm}$)
2× [5] Factor Blocks: Royal Blue / Gold ($h_{\text{vis}} = 29.36\text{ mm}$)
2× [7] Factor Blocks: Crimson / Purple ($h_{\text{vis}} = 35.49\text{ mm}$)
5× Higher Primes: 1 each of [11], [13], [17], [19], [23]
Footprint: 19.0 × 19.0 mm square 0.5U Gridfinity miniblock
Socket Nesting Depth: 1.85 mm (cancels identically on every joint)
Enclosure Box: 3×1×13U Gridfinity Bin (125.5 × 42.0 × 91.0 mm) with prime power lid sockets (Snap-on TPU non-skid feet sold separately)

// CLASSROOM INVESTIGATIONS

Prime vs. Composite: Primes are single indivisible blocks; composites are multi-block stacks.
Commutative Property: $[3] + [5] = [5] + [3] = 15$ (stacking order does not change height).
Greatest Common Divisor: Find $\gcd(18, 24)$ by comparing overlapping blocks $[2] \times [3] = 6$.
Least Common Multiple: Extend stacks until heights equalize; $\text{lcm}(4, 6) = 12$.
Logarithmic Multiplication: Concrete precursor to Napierian logarithms, where adding block heights executes multiplication.

Target Number \(N\)	Prime Blocks Stacked	Visible Height \(\sum h_{\text{vis}}\)	Desk Stacking Top \(Z_{\text{top}}\)	Target Height \(Z_{\text{target}}\)	Alignment Delta
\(N = 2\)	`[2]`	12.64 mm	14.49 mm	14.49 mm	0.000 mm (Exact)
\(N = 4\)	`[2]` + `[2]`	25.29 mm	27.14 mm	27.14 mm	0.000 mm (Exact)
\(N = 6\)	`[2]` + `[3]`	32.68 mm	34.53 mm	34.53 mm	0.000 mm (Exact)
\(N = 10\)	`[2]` + `[5]`	42.00 mm	43.85 mm	43.85 mm	0.000 mm (Exact)
\(N = 20\)	`[2]` + `[2]` + `[5]`	54.64 mm	56.49 mm	56.49 mm	0.000 mm (Exact)
\(N = 50\)	`[2]` + `[5]` + `[5]`	71.36 mm	73.21 mm	73.21 mm	0.000 mm (Exact)
\(N = 100\)	`[2]`² + `[5]`²	84.00 mm	85.85 mm	85.85 mm	0.000 mm (Exact)