Highest Common Factor of 682, 992, 126 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, 992, 126 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 992, 126 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 682, 992, 126 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, 992, 126 is 2.
HCF(682, 992, 126) = 2
HCF of 682, 992, 126 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, 992, 126 is 2.
Highest Common Factor of 682,992,126 is 2
Step 1: Since 992 > 682, we apply the division lemma to 992 and 682, to get
992 = 682 x 1 + 310
Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 310 and 682, to get
682 = 310 x 2 + 62
Step 3: We consider the new divisor 310 and the new remainder 62, and apply the division lemma to get
310 = 62 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 62, the HCF of 682 and 992 is 62
Notice that 62 = HCF(310,62) = HCF(682,310) = HCF(992,682) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 126 > 62, we apply the division lemma to 126 and 62, to get
126 = 62 x 2 + 2
Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 2 and 62, to get
62 = 2 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 62 and 126 is 2
Notice that 2 = HCF(62,2) = HCF(126,62) .
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Frequently Asked Questions on HCF of 682, 992, 126 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, 992, 126?
Answer: HCF of 682, 992, 126 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 992, 126 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 992, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.