Highest Common Factor of 218, 612, 657 using Euclid's algorithm
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 218, 612, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 218, 612, 657 is 1 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 218, 612, 657 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 218, 612, 657 is 1.
HCF(218, 612, 657) = 1
HCF of 218, 612, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 218, 612, 657 is 1.
Highest Common Factor of 218,612,657 is 1
Step 1: Since 612 > 218, we apply the division lemma to 612 and 218, to get
612 = 218 x 2 + 176
Step 2: Since the reminder 218 ≠ 0, we apply division lemma to 176 and 218, to get
218 = 176 x 1 + 42
Step 3: We consider the new divisor 176 and the new remainder 42, and apply the division lemma to get
176 = 42 x 4 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 218 and 612 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(176,42) = HCF(218,176) = HCF(612,218) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 2, we apply the division lemma to 657 and 2, to get
657 = 2 x 328 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 657 is 1
Notice that 1 = HCF(2,1) = HCF(657,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 218, 612, 657 using Euclid's Algorithm
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 218, 612, 657?
Answer: HCF of 218, 612, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 218, 612, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 218, 612, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.