Factorise integers with a smallest-prime-factor sieve, and read off the divisor count, divisor sum, Euler totient, whether the number is squarefree, and how many primes live below the sieve bound. SIEVEFACTORISATIONTOTIENT

Hypotenuse, area, perimeter and both acute angles of a right triangle, from two legs or from a leg and the hypotenuse.

Greatest common divisor and lowest common multiple of two integers, with the Euclidean algorithm shown step by step and the gcd x lcm identity as a check.

Read a four-band resistor from its colours: two digits, a multiplier and a tolerance band, with the nearest E12 and E24 preferred values.

Ratio, speed and torque multipliers and centre distance for a spur gear pair, from tooth counts and pitch diameters.

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