Question
What is the smallest number whose prime factorization has:
(a) three different prime numbers?
(b) four different prime numbers?
(a) three different prime numbers?
(b) four different prime numbers?
✓
Answer
(a) The smallest prime numbers are 2, 3, and 5. To find the smallest number with these primes as factors, multiply them together:
2 × 3 × 5 = 30
So, the smallest number whose prime factorization has three different prime numbers is 30.
(b) The smallest four prime numbers are 2, 3, 5, and 7. To find the smallest number with these primes as factors, multiply them together:
2 × 3 × 5 × 7 = 210
Thus, the smallest number whose prime factorization has four different prime numbers is 210.
2 × 3 × 5 = 30
So, the smallest number whose prime factorization has three different prime numbers is 30.
(b) The smallest four prime numbers are 2, 3, 5, and 7. To find the smallest number with these primes as factors, multiply them together:
2 × 3 × 5 × 7 = 210
Thus, the smallest number whose prime factorization has four different prime numbers is 210.
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