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Highest common factor & least common multiple of 32,56 &72 by prime factorisation?
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Highest common factor & least common multiple of 32,56 &72 by prime fa...
Prime Factorization
To find the highest common factor (HCF) and least common multiple (LCM) of 32, 56, and 72, we start with their prime factorization.
Prime Factorization of Each Number
- 32:
- 32 = 2 × 2 × 2 × 2 × 2 = 2^5
- Prime factors: 2^5
- 56:
- 56 = 2 × 2 × 2 × 7 = 2^3 × 7
- Prime factors: 2^3, 7
- 72:
- 72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2
- Prime factors: 2^3, 3^2
Finding the Highest Common Factor (HCF)
To find the HCF, we take the lowest power of all common prime factors:
- Common prime factor: 2
- Lowest power of 2: 2^3
Thus,
- HCF = 2^3 = 8
Finding the Least Common Multiple (LCM)
To find the LCM, we take the highest power of all prime factors present in any of the numbers:
- Prime factors to consider: 2, 3, 7
- Highest powers:
- 2^5 (from 32)
- 3^2 (from 72)
- 7^1 (from 56)
Now, we calculate the LCM:
- LCM = 2^5 × 3^2 × 7 = 32 × 9 × 7
Calculating step-by-step:
- 32 × 9 = 288
- 288 × 7 = 2016
Thus,
- LCM = 2016
Summary
- Highest Common Factor (HCF): 8
- Least Common Multiple (LCM): 2016
To find the highest common factor (HCF) and least common multiple (LCM) of 32, 56, and 72, we start with their prime factorization.
Prime Factorization of Each Number
- 32:
- 32 = 2 × 2 × 2 × 2 × 2 = 2^5
- Prime factors: 2^5
- 56:
- 56 = 2 × 2 × 2 × 7 = 2^3 × 7
- Prime factors: 2^3, 7
- 72:
- 72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2
- Prime factors: 2^3, 3^2
Finding the Highest Common Factor (HCF)
To find the HCF, we take the lowest power of all common prime factors:
- Common prime factor: 2
- Lowest power of 2: 2^3
Thus,
- HCF = 2^3 = 8
Finding the Least Common Multiple (LCM)
To find the LCM, we take the highest power of all prime factors present in any of the numbers:
- Prime factors to consider: 2, 3, 7
- Highest powers:
- 2^5 (from 32)
- 3^2 (from 72)
- 7^1 (from 56)
Now, we calculate the LCM:
- LCM = 2^5 × 3^2 × 7 = 32 × 9 × 7
Calculating step-by-step:
- 32 × 9 = 288
- 288 × 7 = 2016
Thus,
- LCM = 2016
Summary
- Highest Common Factor (HCF): 8
- Least Common Multiple (LCM): 2016
Community Answer
Highest common factor & least common multiple of 32,56 &72 by prime fa...
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Highest common factor & least common multiple of 32,56 &72 by prime factorisation?
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Highest common factor & least common multiple of 32,56 &72 by prime factorisation? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Highest common factor & least common multiple of 32,56 &72 by prime factorisation? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Highest common factor & least common multiple of 32,56 &72 by prime factorisation?.
Highest common factor & least common multiple of 32,56 &72 by prime factorisation? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Highest common factor & least common multiple of 32,56 &72 by prime factorisation? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Highest common factor & least common multiple of 32,56 &72 by prime factorisation?.
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