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Answer
The prime factors of 60 are 2, 3, and 5.
Solution
To find the prime factors of 60, we first need to determine the prime factorization of 60.
1. Start by dividing 60 by the smallest prime number, which is 2:
\[
60 \div 2 = 30
\]
So, 2 is a prime factor.
2. Next, divide 30 by 2 again:
\[
30 \div 2 = 15
\]
So, 2 is still a prime factor.
3. Now, divide 15 by the next smallest prime number, which is 3:
\[
15 \div 3 = 5
\]
So, 3 is a prime factor.
4. Finally, 5 is also a prime number.
Now we can summarize the prime factorization of 60:
\[
60 = 2^2 \times 3^1 \times 5^1
\]
The prime factors of 60 are 2, 3, and 5.
Thus, the prime numbers that are factors of 60 are:
- 2
- 3
- 5
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Simplify this solution The Deep Dive
The prime factors of 60 are 2, 3, and 5. These numbers are prime because they can only be divided evenly by 1 and themselves. To get to this factorization, you can break down 60 into its prime components: 60 = 2 × 30, 30 = 2 × 15, and 15 = 3 × 5. To further explore prime numbers, did you know that the concept of prime numbers dates back to ancient times? The ancient Greeks studied primes extensively, particularly Euclid, who proved that there are infinitely many prime numbers. Fast forward to today, and primes are crucial in cryptography, ensuring secure communications in our digital age!
