Number theory calculator

Find prime factors, divisor count and sum, and Euler's totient for a positive integer.

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Positive integer

Answer

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Find prime factors, divisor count and sum, and Euler's totient for a positive integer.

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Precision and calculation record

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Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

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Formula and assumptions

Exact integer arithmetic through one billion. The totient counts integers from 1 through n that are coprime to n. For n = 1, the empty prime product is 1 and the totient is 1.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-29

Using Number theory calculator

Find prime factors, divisor count and sum, and Euler's totient for a positive integer.

Exact integer arithmetic through one billion. The totient counts integers from 1 through n that are coprime to n. For n = 1, the empty prime product is 1 and the totient is 1.

Next: Prime factorization calculator

Next: Calculate GCF

A worked example

For positive integer = 60, euler totient = 16.

Before you use the result

Exact integer arithmetic through one billion. The totient counts integers from 1 through n that are coprime to n. For n = 1, the empty prime product is 1 and the totient is 1.

Example results for positive integer

These examples use the formula above. They are reference calculations, not recommended settings.

Positive integer	Euler totient
30	8
60	16
120	32

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