Find the HCF of 105, 135 and 180.
Solution:
Answers
Write all numbers as the product of its prime factors
Prime factors of 105 = 3 . 5 . 7
Prime factors of 135 = 33 . 5
Prime factors of 180 = 22 . 32 . 5
3. Choose the common prime factors with the lowest exponent
Common prime factors: 3 , 5
4. Calculate the Greatest Common Factor or GCF
Remember, to find the GCF of several numbers you must multiply the common prime factors with the lowest exponent.
GCF = 3. 5 = 15
Answer:
HCF = 15
Explanation:
to find the HCF of the following numbers we have to follow these steps:
firstly, we have to express all the numbers as the product of their prime factors. This is called prime factorisation.
105 = 3 × 5 × 7
135 = 3 × 3 × 3 × 5
180 = 2 × 2 × 3 × 3 × 5
Now we have to find the common factors of them from this factorisation.
3 and 5 are common factors. So,
HCF = 3 × 5 = 15
HCF is the compact form of Highest Common factor.
It implies that the numbers having the highest common factor to which they all are divisible.
Some points to be noted about HCF :
HCF of prime numbers is always equal to 1.
HCF must be always equal or less than the given numbers.