Finding HCF of 24, 36, and 102
The Highest Common Factor (HCF) is the largest number that divides two or more numbers without leaving a remainder. We can find the HCF using the prime factorization method.
Step 1: Prime Factorization
Find the prime factors for each number:
- 24: \(2 \times 2 \times 2 \times 3 = 2^3 \times 3\)
- 36: \(2 \times 2 \times 3 \times 3 = 2^2 \times 3^2\)
- 102: \(2 \times 3 \times 17\)
Step 2: Identify Common Factors
Identify the prime factors that are common to all three numbers:
- Common factor: 2
- Common factor: 3
Step 3: Calculate HCF
Multiply the common prime factors, taking the lowest power of each common factor present in any of the factorizations:
- The lowest power of 2 common to all is \(2^1\).
- The lowest power of 3 common to all is \(3^1\).
HCF = \(2^1 \times 3^1 = 2 \times 3 = 6\).
Conclusion
The HCF of 24, 36, and 102 is 6.
Similar Questions
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
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What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
