Answer :
The H.C.F. is the largest number that can divide all the given numbers without leaving a remainder.
In this case, 35 is the largest number that can divide 70, 105, and 175 evenly.
To find the Highest Common Factor (H.C.F.) of 70, 105, and 175, we can use the method of prime factorization.
Prime Factorization
We start by expressing each number as a product of its prime factors.
70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7
Identify Common Prime Factors
Next, we identify the common prime factors among the three numbers.
In this case, the common prime factors are 5 and 7.
Determine the Lowest Power
To find the H.C.F., we take the lowest power of the common prime factors.
The lowest power of 5 is 5.
The lowest power of 7 is 7.
Multiply the Lowest Powers
Finally, we multiply the lowest powers of the common prime factors to find the H.C.F.
H.C.F. = 5 × 7 = 35
Therefore, the H.C.F. of 70, 105, and 175 is 35.
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