Highest Common Factor of 686, 126, 498 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 686, 126, 498 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 126, 498 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 686, 126, 498 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 686, 126, 498 is 2.
HCF(686, 126, 498) = 2
HCF of 686, 126, 498 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 126, 498 is 2.
Highest Common Factor of 686,126,498 is 2
Step 1: Since 686 > 126, we apply the division lemma to 686 and 126, to get
686 = 126 x 5 + 56
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 56 and 126, to get
126 = 56 x 2 + 14
Step 3: We consider the new divisor 56 and the new remainder 14, and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 686 and 126 is 14
Notice that 14 = HCF(56,14) = HCF(126,56) = HCF(686,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 498 > 14, we apply the division lemma to 498 and 14, to get
498 = 14 x 35 + 8
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 8 and 14, to get
14 = 8 x 1 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 498 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(498,14) .
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Frequently Asked Questions on HCF of 686, 126, 498 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 686, 126, 498?
Answer: HCF of 686, 126, 498 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 126, 498 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 126, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.