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 200, 120 i.e. 40 the largest integer that leaves a remainder zero for all numbers.
HCF of 200, 120 is 40 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 200, 120 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 200, 120 is 40.
HCF(200, 120) = 40
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 200, 120 is 40.
Step 1: Since 200 > 120, we apply the division lemma to 200 and 120, to get
200 = 120 x 1 + 80
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 80 and 120, to get
120 = 80 x 1 + 40
Step 3: We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 200 and 120 is 40
Notice that 40 = HCF(80,40) = HCF(120,80) = HCF(200,120) .
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 200, 120?
Answer: HCF of 200, 120 is 40 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 200, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 200, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.