The HCF of the numbers 310 , 208 and 180 is:

Correct option is A

Given:

The numbers are 310, 208, and 180.

Concept Used:

The Highest Common Factor (HCF) of three numbers can be found by finding the HCF of the first two numbers and then finding the HCF of the result with the third number.

Solution:

The HCF of 310 and 208.

By Euclidean algorithm:

​$$310 \div 208 = 1 \quad \text{(remainder }310 - 208 = 102) \\ \ \\ 208 \div 102 = 2 \quad \text{(remainder} 208 - 2 \times 102 = 4) \\ \ \\ 102 \div 4 = 25 \quad \text{(remainder} 102 - 25 \times 4 = 2) \\ \ \\ 4 \div 2 = 2 \quad \text{(remainder 4 - 2} \times 2 = 0)$$​​

So, the HCF of 310 and 208 is 2.

Now,  $$180 \div 2 = 90 \quad \text{(remainder 0)}$$​​

So, the HCF of 2 and 180 is 2.

Thus, the HCF of 310, 208, and 180 is 2.