Highest Common Factor of 684, 475, 212, 209 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 684, 475, 212, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 475, 212, 209 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 684, 475, 212, 209 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 684, 475, 212, 209 is 1.
HCF(684, 475, 212, 209) = 1
HCF of 684, 475, 212, 209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 475, 212, 209 is 1.
Highest Common Factor of 684,475,212,209 is 1
Step 1: Since 684 > 475, we apply the division lemma to 684 and 475, to get
684 = 475 x 1 + 209
Step 2: Since the reminder 475 ≠ 0, we apply division lemma to 209 and 475, to get
475 = 209 x 2 + 57
Step 3: We consider the new divisor 209 and the new remainder 57, and apply the division lemma to get
209 = 57 x 3 + 38
We consider the new divisor 57 and the new remainder 38,and apply the division lemma to get
57 = 38 x 1 + 19
We consider the new divisor 38 and the new remainder 19,and apply the division lemma to get
38 = 19 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 684 and 475 is 19
Notice that 19 = HCF(38,19) = HCF(57,38) = HCF(209,57) = HCF(475,209) = HCF(684,475) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 212 > 19, we apply the division lemma to 212 and 19, to get
212 = 19 x 11 + 3
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 3 and 19, to get
19 = 3 x 6 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 212 is 1
Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(212,19) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get
209 = 1 x 209 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1
Notice that 1 = HCF(209,1) .
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Frequently Asked Questions on HCF of 684, 475, 212, 209 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 684, 475, 212, 209?
Answer: HCF of 684, 475, 212, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 475, 212, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 475, 212, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.