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Problem #81 · October 16, 2026

EKUB — greatest common divisor and EKUK — least common multiple

Which of the following is the prime factorization of the number 84?
  1. A22⋅3⋅72^2 \cdot 3 \cdot 7
  2. B2⋅3⋅142 \cdot 3 \cdot 14
  3. C4⋅214 \cdot 21
  4. D2⋅422 \cdot 42
  5. E23⋅3⋅72^3 \cdot 3 \cdot 7

WORKED EXAMPLE

Solution

We divide successively: 84:2=4284 : 2 = 42, 42:2=2142 : 2 = 21, 21:3=721 : 3 = 7, and 7 is a prime number. Therefore 84=22⋅3⋅784 = 2^2 \cdot 3 \cdot 7. In a prime factorization, only prime numbers may appear.
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