Answer: Option B
To find the H.C.F. of the given numbers, we need to find the product of the highest powers of all the common prime factors.
Let's list out the prime factors of each number:
2⁴ × 3² × 5³ × 7 = 2² × (2 × 3)² × 5³ × 7¹2³ × 3³ × 5² × 7² = (2 × 3)³ × 5² × 7²3 × 5 × 7 × 11Now, we can see that the common prime factors among all the given numbers are 3, 5, and 7.
For 3, we take the lowest power of 3 that occurs in any of the given numbers, which is 1 in the third number.For 5, we take the lowest power of 5 that occurs in any of the given numbers, which is 2 in the second number.For 7, we take the lowest power of 7 that occurs in any of the given numbers, which is 1 in the first and third numbers.Thus, the product of the highest powers of the common prime factors is:
H.C.F. = 3¹ × 5² × 7¹ = 105
Therefore, the correct answer is option B, 105.
To summarize, we can use the following steps to find the H.C.F. of given numbers:
Find the prime factors of each number.Identify the common prime factors among all the given numbers.Take the lowest power of each common prime factor that occurs in any of the given numbers.Multiply these powers together to get the H.C.F. of the given numbers.If you think the solution is wrong then please provide your own solution below in the comments section .