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24, 36 మరియు 102ల గ.సా.భా. కనుగొనండి.
12
6
8
4
6
Check the smallest difference between any two numbers. The HCF must be a factor of that difference. Here, 36−24=12. Since 12 does not divide 102, check the factors of 12 (12, 6, 4, 3, 2, 1). 6 is the largest factor of 12 that divides all three numbers.
Numbers to find HCF are 24, 36, and 102.
HCF(a,b,c)=Highest common prime factor raised to the lowest power
Check the smallest difference between any two numbers. The HCF must be a factor of that difference. Here, 36−24=12. Since 12 does not divide 102, check the factors of 12 (12, 6, 4, 3, 2, 1). 6 is the largest factor of 12 that divides all three numbers.
Students often pick the HCF of only two numbers (e.g., 24 and 36 give 12) and fail to verify if it divides the third number (102).
Prime Factorization
Break down each number into its prime factors: 24=23×3, 36=22×32, and 102=2×3×17.
24=23×31,36=22×32,102=21×31×171
Identify Common Factors
Identify the common prime bases present in all numbers, which are 2 and 3.
Common Bases={2,3}
Apply HCFRule
Take the lowest exponent for each common prime base: for 2, it is 21; for 3, it is 31.
HCF=21×31=6
B is correct because the greatest common divisor that divides 24, 36, and 102 without leaving a remainder is 6.
HCF is essential for finding the largest size of tiles in a room or the largest length of a measuring rod in measurement problems.