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Three numbers are co-prime to each other, such that the product of first two co-prime numbers is 459 and the product of last two coprime numbers is 621. What must be the sum of these three co-prime numbers?
- a)57
- b)67
- c)79
- d)81
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Three numbers are co-prime to each other, such that the product of fir...
Let, x, y, z be the three co-prime numbers.
According to the question, xy = 459 and yz = 621 Since, y is common between xy and yz. So, y = H.C.F of 459, 621 = 27 Therefore, x = 459/y = 459/27 = 17 And z = 621/y = 621/27 = 23 Sum of these three co-prime numbers = x + y + z = 17 + 27 + 23 = 67 Hence, option (b) is the correct answer.
According to the question, xy = 459 and yz = 621 Since, y is common between xy and yz. So, y = H.C.F of 459, 621 = 27 Therefore, x = 459/y = 459/27 = 17 And z = 621/y = 621/27 = 23 Sum of these three co-prime numbers = x + y + z = 17 + 27 + 23 = 67 Hence, option (b) is the correct answer.
Most Upvoted Answer
Three numbers are co-prime to each other, such that the product of fir...
Given Information:
- The product of the first two co-prime numbers is 459.
- The product of the last two co-prime numbers is 621.
Solution:
Finding the Co-prime Numbers:
- Let's find the prime factors of 459 and 621.
- The prime factorization of 459 is 3 x 3 x 3 x 17.
- The prime factorization of 621 is 3 x 3 x 3 x 3 x 23.
Identifying the Co-prime Numbers:
- From the prime factorization, we can see that the co-prime numbers are (3, 17) and (3, 23).
- Therefore, the three co-prime numbers are 3, 17, and 23.
Calculating the Sum:
- The sum of the three co-prime numbers is 3 + 17 + 23 = 43.
- Therefore, the correct answer is option B (67).
- The product of the first two co-prime numbers is 459.
- The product of the last two co-prime numbers is 621.
Solution:
Finding the Co-prime Numbers:
- Let's find the prime factors of 459 and 621.
- The prime factorization of 459 is 3 x 3 x 3 x 17.
- The prime factorization of 621 is 3 x 3 x 3 x 3 x 23.
Identifying the Co-prime Numbers:
- From the prime factorization, we can see that the co-prime numbers are (3, 17) and (3, 23).
- Therefore, the three co-prime numbers are 3, 17, and 23.
Calculating the Sum:
- The sum of the three co-prime numbers is 3 + 17 + 23 = 43.
- Therefore, the correct answer is option B (67).
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