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
- Three bells ring at intervals of 15, 30 and 45 minutes respectively. At what time will they ring together again, if they rang simultaneously at 8.00 AM?
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
