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 612, 120, 202 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 120, 202 is 2 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 612, 120, 202 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 612, 120, 202 is 2.
HCF(612, 120, 202) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 120, 202 is 2.
Step 1: Since 612 > 120, we apply the division lemma to 612 and 120, to get
612 = 120 x 5 + 12
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 12 and 120, to get
120 = 12 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 612 and 120 is 12
Notice that 12 = HCF(120,12) = HCF(612,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 202 > 12, we apply the division lemma to 202 and 12, to get
202 = 12 x 16 + 10
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 10 and 12, to get
12 = 10 x 1 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 202 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(202,12) .
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 612, 120, 202?
Answer: HCF of 612, 120, 202 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 120, 202 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 120, 202 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.