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A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible?
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A remainder (m - 3) is obtained when 72 is divided by m, where m is a ...
Solution:
Given, a remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3.
Let's write this down in an equation form:
72 = qm + (m - 3), where q is a natural number
Simplifying the equation, we get:
75 = qm + m
75 = m(q + 1)
So, m divides 75.
There are only a limited number of factors of 75, and we need to check which ones are greater than 3, as m is a natural number greater than 3.
Factors of 75 are: 1, 3, 5, 15, 25, 75.
Out of these, only 5, 15, 25 and 75 are greater than 3.
Therefore, there are four different values of m that are possible: 5, 15, 25, and 75.
Hence, the answer is 4.
Given, a remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3.
Let's write this down in an equation form:
72 = qm + (m - 3), where q is a natural number
Simplifying the equation, we get:
75 = qm + m
75 = m(q + 1)
So, m divides 75.
There are only a limited number of factors of 75, and we need to check which ones are greater than 3, as m is a natural number greater than 3.
Factors of 75 are: 1, 3, 5, 15, 25, 75.
Out of these, only 5, 15, 25 and 75 are greater than 3.
Therefore, there are four different values of m that are possible: 5, 15, 25, and 75.
Hence, the answer is 4.
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A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible?
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A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible?.
A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A remainder (m - 3) is obtained when 72 is divided by m, where m is a natural number greater than 3. How many different values of m are possible?.
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