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Support this statement with example
If a number is divisible by two coprime number then it is divisible by their product also?
If a number is divisible by two coprime number then it is divisible by their product also?
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Support this statement with example If a number is divisible by two co...
Explanation:
To prove that if a number is divisible by two coprime numbers, then it is divisible by their product, we can use the concept of prime factorization.
Prime Factorization:
- Any integer greater than 1 can be expressed as a product of prime numbers.
- For example, 12 can be expressed as 2 * 2 * 3, where 2 and 3 are prime numbers.
Proof:
- Let the two coprime numbers be a and b, and their product be c (c = a * b).
- If a number n is divisible by both a and b, it means that n can be expressed as n = a * x and n = b * y, where x and y are integers.
- Since a and b are coprime, the only common factor between them is 1.
- Therefore, n = a * b * z, where z is an integer.
- This shows that n is divisible by the product of a and b, which is c.
Example:
- Let's take two coprime numbers, 3 and 5, and their product is 15.
- If a number, say 30, is divisible by both 3 and 5, then it is also divisible by their product 15.
- 30 = 3 * 10 and 30 = 5 * 6, therefore 30 = 3 * 5 * 2.
This example illustrates how a number divisible by two coprime numbers is also divisible by their product.
To prove that if a number is divisible by two coprime numbers, then it is divisible by their product, we can use the concept of prime factorization.
Prime Factorization:
- Any integer greater than 1 can be expressed as a product of prime numbers.
- For example, 12 can be expressed as 2 * 2 * 3, where 2 and 3 are prime numbers.
Proof:
- Let the two coprime numbers be a and b, and their product be c (c = a * b).
- If a number n is divisible by both a and b, it means that n can be expressed as n = a * x and n = b * y, where x and y are integers.
- Since a and b are coprime, the only common factor between them is 1.
- Therefore, n = a * b * z, where z is an integer.
- This shows that n is divisible by the product of a and b, which is c.
Example:
- Let's take two coprime numbers, 3 and 5, and their product is 15.
- If a number, say 30, is divisible by both 3 and 5, then it is also divisible by their product 15.
- 30 = 3 * 10 and 30 = 5 * 6, therefore 30 = 3 * 5 * 2.
This example illustrates how a number divisible by two coprime numbers is also divisible by their product.
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Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also?
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Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also?.
Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Support this statement with example If a number is divisible by two coprime number then it is divisible by their product also?.
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