Highest Common Factor of 684, 418, 208 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, 418, 208 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 418, 208 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 684, 418, 208 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, 418, 208 is 2.
HCF(684, 418, 208) = 2
HCF of 684, 418, 208 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, 418, 208 is 2.
Highest Common Factor of 684,418,208 is 2
Step 1: Since 684 > 418, we apply the division lemma to 684 and 418, to get
684 = 418 x 1 + 266
Step 2: Since the reminder 418 ≠ 0, we apply division lemma to 266 and 418, to get
418 = 266 x 1 + 152
Step 3: We consider the new divisor 266 and the new remainder 152, and apply the division lemma to get
266 = 152 x 1 + 114
We consider the new divisor 152 and the new remainder 114,and apply the division lemma to get
152 = 114 x 1 + 38
We consider the new divisor 114 and the new remainder 38,and apply the division lemma to get
114 = 38 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 684 and 418 is 38
Notice that 38 = HCF(114,38) = HCF(152,114) = HCF(266,152) = HCF(418,266) = HCF(684,418) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 208 > 38, we apply the division lemma to 208 and 38, to get
208 = 38 x 5 + 18
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 18 and 38, to get
38 = 18 x 2 + 2
Step 3: We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 38 and 208 is 2
Notice that 2 = HCF(18,2) = HCF(38,18) = HCF(208,38) .
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Frequently Asked Questions on HCF of 684, 418, 208 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, 418, 208?
Answer: HCF of 684, 418, 208 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 418, 208 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 418, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.