Highest Common Factor of 682, 392, 123 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 682, 392, 123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 392, 123 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 682, 392, 123 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 682, 392, 123 is 1.
HCF(682, 392, 123) = 1
HCF of 682, 392, 123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 392, 123 is 1.
Highest Common Factor of 682,392,123 is 1
Step 1: Since 682 > 392, we apply the division lemma to 682 and 392, to get
682 = 392 x 1 + 290
Step 2: Since the reminder 392 ≠ 0, we apply division lemma to 290 and 392, to get
392 = 290 x 1 + 102
Step 3: We consider the new divisor 290 and the new remainder 102, and apply the division lemma to get
290 = 102 x 2 + 86
We consider the new divisor 102 and the new remainder 86,and apply the division lemma to get
102 = 86 x 1 + 16
We consider the new divisor 86 and the new remainder 16,and apply the division lemma to get
86 = 16 x 5 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 682 and 392 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(86,16) = HCF(102,86) = HCF(290,102) = HCF(392,290) = HCF(682,392) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 123 > 2, we apply the division lemma to 123 and 2, to get
123 = 2 x 61 + 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 123 is 1
Notice that 1 = HCF(2,1) = HCF(123,2) .
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Frequently Asked Questions on HCF of 682, 392, 123 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 682, 392, 123?
Answer: HCF of 682, 392, 123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 392, 123 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 392, 123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.