Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 120, 180 i.e. 60 the largest integer that leaves a remainder zero for all numbers.
HCF of 120, 180 is 60 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 120, 180 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 120, 180 is 60.
HCF(120, 180) = 60
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 120, 180 is 60.
Step 1: Since 180 > 120, we apply the division lemma to 180 and 120, to get
180 = 120 x 1 + 60
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 60 and 120, to get
120 = 60 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 120 and 180 is 60
Notice that 60 = HCF(120,60) = HCF(180,120) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 120, 180?
Answer: HCF of 120, 180 is 60 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 120, 180 using Euclid's Algorithm?
Answer: For arbitrary numbers 120, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.