Highest Common Factor of 126, 498, 274 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 126, 498, 274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 498, 274 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 126, 498, 274 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 126, 498, 274 is 2.
HCF(126, 498, 274) = 2
HCF of 126, 498, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 498, 274 is 2.
Highest Common Factor of 126,498,274 is 2
Step 1: Since 498 > 126, we apply the division lemma to 498 and 126, to get
498 = 126 x 3 + 120
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 120 and 126, to get
126 = 120 x 1 + 6
Step 3: We consider the new divisor 120 and the new remainder 6, and apply the division lemma to get
120 = 6 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 126 and 498 is 6
Notice that 6 = HCF(120,6) = HCF(126,120) = HCF(498,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 6, we apply the division lemma to 274 and 6, to get
274 = 6 x 45 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 274 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(274,6) .
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Frequently Asked Questions on HCF of 126, 498, 274 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 126, 498, 274?
Answer: HCF of 126, 498, 274 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 498, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 498, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.