Exercise 371Number theory › Divisibility and gcdHigh schoolAdded 2 Nov 2026

divisibility of three numbers

#divisibility#three numbers#prime factorization

Statement

Compute $\divisibility(540,468,396)$ .

Hint

Compute $\divisibility(540,468)$ first, then take the divisibility with $396$ . Alternatively, use prime factorizations.

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Prime factorizations.
$540=2^2\cdot3^3\cdot5,\qquad 468=2^2\cdot3^2\cdot13,\qquad 396=2^2\cdot3^2\cdot11.$

divisibility. Take the smallest exponent of each common prime:
$\divisibility=2^2\cdot3^2=4\cdot9=36.$

Remark. This is the maximum number of identical bags one can form with $540$ red, $468$ green, and $396$ yellow candies.