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If a and b are two positive co-prime integers such that a = 12b , then hcf of [a,12] is ...
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If a and b are two positive co-prime integers such that a = 12b , then...
**Solution:**
Given, a = 12b and a, b are co-prime positive integers.
To find the HCF of [a, 12], we need to find the highest common factor of a and 12.
Let's break down the solution into multiple steps:
**Step 1: Determine the prime factors of 12**
The prime factors of 12 are 2 and 3.
**Step 2: Express a in terms of its prime factors**
Since a = 12b, we can express a in terms of its prime factors as:
a = (2^2) * (3^1) * b
**Step 3: Determine the prime factors of a**
The prime factors of a are 2 and 3.
**Step 4: Determine the common factors of a and 12**
The common factors of a and 12 are the prime factors that appear in both numbers. In this case, the common factors are 2 and 3.
**Step 5: Determine the highest common factor (HCF)**
The HCF is the product of the common factors raised to their lowest exponent. In this case, the HCF of [a, 12] is:
HCF = (2^1) * (3^1) = 2 * 3 = 6
Therefore, the HCF of [a, 12] is 6.
**Explanation:**
The given information states that a = 12b, which means that a is a multiple of 12. In other words, a can be expressed as a product of 12 and some positive integer.
To find the HCF of [a, 12], we need to determine the highest common factor of a and 12. The prime factors of 12 are 2 and 3. By expressing a in terms of its prime factors, we can see that a also has prime factors of 2 and 3.
The common factors of a and 12 are the prime factors that appear in both numbers. In this case, the common factors are 2 and 3. The HCF is obtained by taking the product of the common factors raised to their lowest exponent. Hence, the HCF of [a, 12] is 6.
It is important to note that the given condition of a and b being co-prime integers is not utilized in this question.
Given, a = 12b and a, b are co-prime positive integers.
To find the HCF of [a, 12], we need to find the highest common factor of a and 12.
Let's break down the solution into multiple steps:
**Step 1: Determine the prime factors of 12**
The prime factors of 12 are 2 and 3.
**Step 2: Express a in terms of its prime factors**
Since a = 12b, we can express a in terms of its prime factors as:
a = (2^2) * (3^1) * b
**Step 3: Determine the prime factors of a**
The prime factors of a are 2 and 3.
**Step 4: Determine the common factors of a and 12**
The common factors of a and 12 are the prime factors that appear in both numbers. In this case, the common factors are 2 and 3.
**Step 5: Determine the highest common factor (HCF)**
The HCF is the product of the common factors raised to their lowest exponent. In this case, the HCF of [a, 12] is:
HCF = (2^1) * (3^1) = 2 * 3 = 6
Therefore, the HCF of [a, 12] is 6.
**Explanation:**
The given information states that a = 12b, which means that a is a multiple of 12. In other words, a can be expressed as a product of 12 and some positive integer.
To find the HCF of [a, 12], we need to determine the highest common factor of a and 12. The prime factors of 12 are 2 and 3. By expressing a in terms of its prime factors, we can see that a also has prime factors of 2 and 3.
The common factors of a and 12 are the prime factors that appear in both numbers. In this case, the common factors are 2 and 3. The HCF is obtained by taking the product of the common factors raised to their lowest exponent. Hence, the HCF of [a, 12] is 6.
It is important to note that the given condition of a and b being co-prime integers is not utilized in this question.
Community Answer
If a and b are two positive co-prime integers such that a = 12b , then...
Is it 12
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If a and b are two positive co-prime integers such that a = 12b , then hcf of [a,12] is ...?
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If a and b are two positive co-prime integers such that a = 12b , then hcf of [a,12] is ...? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If a and b are two positive co-prime integers such that a = 12b , then hcf of [a,12] is ...? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are two positive co-prime integers such that a = 12b , then hcf of [a,12] is ...?.
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