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Q.

Find HCF of 70 and 245 using the fundamental theorem of arithmetic.


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a

35

b

30

c

15

d

25  

answer is A.

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Detailed Solution

Given, numbers are 70 and 245.
We need to find the HCF of these numbers using the fundamental theorem of arithmetic.
According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number or may be written in the form of primes.
This means that all natural numbers can be represented as the product of their prime components.
Using the fundamental theorem of arithmetic, we can write the given integers as a product of their prime factors,
70=2×5×7 245=5×7×7 Here, the common factors of 70 and 245 are 5 and 7.
So, HCF=5×7 ⇒HCF=35 Therefore, HCF of 70 and 245 is 35.
Hence, option 1 is correct.
 
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