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What is the smallest prime factor of (842−132)?
- a)13
- b)59
- c)61
- d)71
- e)97
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the smallest prime factor of (842−132)?a)13b)59c)61d)71e...
Calculation of the Expression
To find the smallest prime factor of (842 - 132), we first need to perform the subtraction.
- 842 - 132 = 710.
Finding Prime Factors
Next, we will find the prime factors of 710. A prime factor is a prime number that divides another number exactly, without leaving a remainder.
Step-by-Step Factorization
1. Check divisibility by 2:
- 710 is even, thus divisible by 2.
- 710 ÷ 2 = 355.
2. Check 355 for further factors:
- 355 is odd, so not divisible by 2.
- Check divisibility by 3: Sum of digits (3 + 5 + 5 = 13) is not divisible by 3.
- Check divisibility by 5: Ends in 5, thus divisible by 5.
- 355 ÷ 5 = 71.
3. Check if 71 is prime:
- 71 is not divisible by 2, 3, 5, or 7 (the primes less than √71).
- Therefore, 71 is a prime number.
Summary of Factors
From the factorization, we have:
- The factors of 710 are 2, 5, and 71.
- Among these, the prime factors are 2, 5, and 71.
Conclusion
To find the smallest prime factor, we compare them:
- 2 (smallest)
- 5
- 71
Thus, the smallest prime factor of (842 - 132) is 2. However, if you are looking for the smallest prime factor from the provided options, the correct prime factor from the list is 71, which is option 'D'.
To find the smallest prime factor of (842 - 132), we first need to perform the subtraction.
- 842 - 132 = 710.
Finding Prime Factors
Next, we will find the prime factors of 710. A prime factor is a prime number that divides another number exactly, without leaving a remainder.
Step-by-Step Factorization
1. Check divisibility by 2:
- 710 is even, thus divisible by 2.
- 710 ÷ 2 = 355.
2. Check 355 for further factors:
- 355 is odd, so not divisible by 2.
- Check divisibility by 3: Sum of digits (3 + 5 + 5 = 13) is not divisible by 3.
- Check divisibility by 5: Ends in 5, thus divisible by 5.
- 355 ÷ 5 = 71.
3. Check if 71 is prime:
- 71 is not divisible by 2, 3, 5, or 7 (the primes less than √71).
- Therefore, 71 is a prime number.
Summary of Factors
From the factorization, we have:
- The factors of 710 are 2, 5, and 71.
- Among these, the prime factors are 2, 5, and 71.
Conclusion
To find the smallest prime factor, we compare them:
- 2 (smallest)
- 5
- 71
Thus, the smallest prime factor of (842 - 132) is 2. However, if you are looking for the smallest prime factor from the provided options, the correct prime factor from the list is 71, which is option 'D'.
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Community Answer
What is the smallest prime factor of (842−132)?a)13b)59c)61d)71e...
Step 1: Simplify the Expression
The expression 84² - 13² is a difference of squares, which can be factored using the formula:
a² - b² = (a + b)(a - b)
The expression 84² - 13² is a difference of squares, which can be factored using the formula:
a² - b² = (a + b)(a - b)
Applying this formula:
84² - 13² = (84 + 13)(84 - 13) = 97 × 71
84² - 13² = (84 + 13)(84 - 13) = 97 × 71
Step 2: Analyze the Factors
Now, we have:
84² - 13² = 97 × 71
Now, we have:
84² - 13² = 97 × 71
- 97:
- Prime Check: 97 is a prime number (it has no divisors other than 1 and itself).
- 71:
- Prime Check: 71 is also a prime number.
Step 3: Determine the Smallest Prime Factor
From the factorization:
84² - 13² = 97 × 71
From the factorization:
84² - 13² = 97 × 71
Both 97 and 71 are prime numbers. Among these:
Smallest Prime Factor = 71
Smallest Prime Factor = 71
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What is the smallest prime factor of (842−132)?a)13b)59c)61d)71e)97Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the smallest prime factor of (842−132)?a)13b)59c)61d)71e)97Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the smallest prime factor of (842−132)?a)13b)59c)61d)71e)97Correct answer is option 'D'. Can you explain this answer?.
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