what are the smallest and greatest factors of 340
What are the smallest and greatest factors of 340?
Answer:
To determine the smallest and greatest factors of 340, we first need to understand what a factor is. A factor is a number that divides another number exactly, without leaving a remainder. Let’s explore the factors of 340 comprehensively.
Prime Factorization
The prime factorization of a number helps us understand its factors more clearly. For 340, let’s find its prime factors:
-
Divide by the smallest prime number (2):
340 is even, so divide by 2:
340 \div 2 = 170 -
Divide 170 by 2:
170 is also even, so divide by 2 again:
170 \div 2 = 85 -
Divide by the next smallest prime number (5):
85 ends in 5, so divide by 5:
85 \div 5 = 17 -
Check for divisibility by 17:
17 is a prime number.
The prime factorization of 340 is thus (2^2 \times 5 \times 17).
Identifying the Factors
Using our prime factorization, we can generate all the factors of 340. The factors are obtained by multiplying the prime factors in all possible combinations:
- 1 (always a factor of any number)
- 2 (2^1)
- 4 (2^2)
- 5
- 10 (2 \times 5)
- 17
- 20 (2^2 \times 5)
- 34 (2 \times 17)
- 68 (2^2 \times 17)
- 85 (5 \times 17)
- 170 (2 \times 5 \times 17)
- 340
Smallest and Greatest Factors
From the list above:
- The smallest factor of 340 is 1.
- The greatest factor of 340 is 340 itself.
Conclusion
Every number has at least two factors: 1 and itself. For the number 340, you have multiple factors, with 1 and 340 being the smallest and greatest, respectively. Using the prime factorization approach, you can also determine that the factors are derived from multiplying the number’s prime factors in various combinations.
If you have any more questions about factors or need further clarification on mathematical concepts, feel free to ask!