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Q.

The HCF of 34 and 102 is {fill _number}.


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Detailed Solution

Concept- The HCF is 34. Identify the prime factors that make up 34 and 102. Once you have chosen all the factors that appear in both the prime factorizations of 34 and 102, you can go on. To determine the HCF of the two numbers, multiply these common factors.
We must determine the 34 and 102 HCF.
Let's look at the definition of HCF first.
The greatest positive integer that divides each integer is known as the HCF, or Highest Common Factor, of two or more integers that are not all zero.
We must ascertain the prime factorizations of 34 and 102 in order to determine HCF.
We will start by determining 34's prime factorization.
So, 34 can be written as: 34=2×1734=2×17
So, 102 can be written as: 102=2×3×17 We now need to identify the elements that both the prime factorizations of 34 and 102 have in common.
We can observe that both prime factorizations of 217 share this property.
The HCF is therefore 217=34.
Consequently, 34 is the GCF of 34 and 102.
Hence, the correct option is 34.
 ExamType: CBSE
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