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

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

## 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 83
Copy notation 8 9
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 E84 E158
Bashicu matrix system (0)(0)(0)(0)(0) (0)(0)(0)(0)(0)
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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