Highest Common Factor of 411, 684, 702 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 411, 684, 702 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 411, 684, 702 is 3 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 411, 684, 702 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 411, 684, 702 is 3.
HCF(411, 684, 702) = 3
HCF of 411, 684, 702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 411, 684, 702 is 3.
Highest Common Factor of 411,684,702 is 3
Step 1: Since 684 > 411, we apply the division lemma to 684 and 411, to get
684 = 411 x 1 + 273
Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 273 and 411, to get
411 = 273 x 1 + 138
Step 3: We consider the new divisor 273 and the new remainder 138, and apply the division lemma to get
273 = 138 x 1 + 135
We consider the new divisor 138 and the new remainder 135,and apply the division lemma to get
138 = 135 x 1 + 3
We consider the new divisor 135 and the new remainder 3,and apply the division lemma to get
135 = 3 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 411 and 684 is 3
Notice that 3 = HCF(135,3) = HCF(138,135) = HCF(273,138) = HCF(411,273) = HCF(684,411) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 702 > 3, we apply the division lemma to 702 and 3, to get
702 = 3 x 234 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 702 is 3
Notice that 3 = HCF(702,3) .
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Frequently Asked Questions on HCF of 411, 684, 702 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 411, 684, 702?
Answer: HCF of 411, 684, 702 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 411, 684, 702 using Euclid's Algorithm?
Answer: For arbitrary numbers 411, 684, 702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.