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When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes? a)24 b)124 c)18 d)None of these Correct answer is option 'C'. Can you explain this answer?
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When 7179 and 9699 are divided by another natural number N , remainder...
To solve this problem, we need to find the values of N that will result in the same remainder when dividing both 7179 and 9699.
Let's first find the remainder when dividing 7179 and 9699 by N.
For 7179:
Let's assume the remainder is R1 when dividing 7179 by N.
So, 7179 = N * Q1 + R1
where Q1 is the quotient when dividing 7179 by N.
For 9699:
Let's assume the remainder is R2 when dividing 9699 by N.
So, 9699 = N * Q2 + R2
where Q2 is the quotient when dividing 9699 by N.
According to the problem, R1 = R2.
Now, let's simplify the equations and put them together:
N * Q1 + R1 = N * Q2 + R2
Rearranging the equation, we get:
N * (Q1 - Q2) = R2 - R1
Since R1 = R2, the right side of the equation becomes zero:
N * (Q1 - Q2) = 0
For the equation to be true, either N = 0 or (Q1 - Q2) = 0.
Now, we know that N cannot be zero because it is a natural number. So, the only possibility is (Q1 - Q2) = 0.
(Q1 - Q2) = 0 means that the quotients Q1 and Q2 are equal when dividing 7179 and 9699 by N.
To find the values of N that satisfy this condition, we need to consider the factors of 7179 and 9699.
Prime factorization of 7179: 3^2 * 797
Prime factorization of 9699: 3^2 * 1077
To have the same quotient when dividing by N, the prime factorization of N should include the common factors of 7179 and 9699, which are 3^2.
Since N is a natural number, the possible values of N are the divisors of 3^2, which are 1, 3, and 9.
Among these values, only 9 ends with one or more than one zeroes.
Therefore, the correct answer is option C) 18.
Let's first find the remainder when dividing 7179 and 9699 by N.
For 7179:
Let's assume the remainder is R1 when dividing 7179 by N.
So, 7179 = N * Q1 + R1
where Q1 is the quotient when dividing 7179 by N.
For 9699:
Let's assume the remainder is R2 when dividing 9699 by N.
So, 9699 = N * Q2 + R2
where Q2 is the quotient when dividing 9699 by N.
According to the problem, R1 = R2.
Now, let's simplify the equations and put them together:
N * Q1 + R1 = N * Q2 + R2
Rearranging the equation, we get:
N * (Q1 - Q2) = R2 - R1
Since R1 = R2, the right side of the equation becomes zero:
N * (Q1 - Q2) = 0
For the equation to be true, either N = 0 or (Q1 - Q2) = 0.
Now, we know that N cannot be zero because it is a natural number. So, the only possibility is (Q1 - Q2) = 0.
(Q1 - Q2) = 0 means that the quotients Q1 and Q2 are equal when dividing 7179 and 9699 by N.
To find the values of N that satisfy this condition, we need to consider the factors of 7179 and 9699.
Prime factorization of 7179: 3^2 * 797
Prime factorization of 9699: 3^2 * 1077
To have the same quotient when dividing by N, the prime factorization of N should include the common factors of 7179 and 9699, which are 3^2.
Since N is a natural number, the possible values of N are the divisors of 3^2, which are 1, 3, and 9.
Among these values, only 9 ends with one or more than one zeroes.
Therefore, the correct answer is option C) 18.
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When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes? a)24 b)124 c)18 d)None of these Correct answer is option 'C'. Can you explain this answer?
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When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes? a)24 b)124 c)18 d)None of these Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes? a)24 b)124 c)18 d)None of these Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When 7179 and 9699 are divided by another natural number N , remainder obtained is same. How many values of N will be ending with one or more than one zeroes? a)24 b)124 c)18 d)None of these Correct answer is option 'C'. Can you explain this answer?.
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