Not to be confused with [[:Factorization (algebra)]].


Factor is equal to 100! ≈ 9.33262154537 × 10157, where ! denotes factorial. The term was coined by Yabuszko.[1]

Decimal expansion

93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000

Etymology

The name of the number is a mix of "factorial" and nordic god "thor".

Approximations

Notation Lower bound Upper bound
Scientific notation \(9.332\times10^{157}\) \(9.333\times10^{157}\)
Arrow notation \(82\uparrow 84\) \(10\uparrow 158\)
Steinhaus-Moser Notation 82[3] 83[3]
Copy notation 8[158] 9[158]
Chained arrow notation \(82 \rightarrow 84\) \(10 \rightarrow 158\)
Taro's multivariable Ackermann function A(3,518) A(3,519)
Pound-Star Notation #*((3))*9 #*((4))*9
BEAF {82,84} {10,158}
Hyper-E notation E[82]84 E158
Bashicu matrix system (0)(0)(0)(0)(0)[86409] (0)(0)(0)(0)(0)[86410]
Hyperfactorial array notation 100!
Fast-growing hierarchy \(f_2(515)\) \(f_2(516)\)
Hardy hierarchy \(H_{\omega^2}(515)\) \(H_{\omega^2}(516)\)
Slow-growing hierarchy \(g_{\omega^{\omega^2+\omega5+7}}(10)\) \(g_{\omega^{\omega^2+\omega5+8}}(10)\)

Sources

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