Find the HCF of 2³ x 3² x 5 x 7^2; 2² x 5² x 7³ and 2³ x 5³ x 7².Options :A] 940B] 980C] 930D] 925
Question
Find the HCF of 2³ x 3² x 5 x 7²; 2² x 5² x 7³ and 2³ x 5³ x 7².
Options :
A] 940
B] 980
C] 930
D] 925
Solution
To find the Highest Common Factor (HCF) of the given numbers, we need to take the lowest power of each prime factor common to all the numbers.
The prime factors are 2, 3, 5, and 7.
For 2, the lowest power is 2 (from 2²). For 3, the lowest power is 0 (since 3 is not a factor in the second and third numbers). For 5, the lowest power is 1 (from 5¹). For 7, the lowest power is 2 (from 7²).
So, the HCF is 2² x 3⁰ x 5¹ x 7² = 4 x 1 x 5 x 49 = 980.
So, the correct option is B] 980.
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