Highest Common Factor of 776, 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 776, 498 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 776, 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 776, 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 776, 498 is 2.
HCF(776, 498) = 2
HCF of 776, 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 776, 498 is 2.
Highest Common Factor of 776,498 is 2
Step 1: Since 776 > 498, we apply the division lemma to 776 and 498, to get
776 = 498 x 1 + 278
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 278 and 498, to get
498 = 278 x 1 + 220
Step 3: We consider the new divisor 278 and the new remainder 220, and apply the division lemma to get
278 = 220 x 1 + 58
We consider the new divisor 220 and the new remainder 58,and apply the division lemma to get
220 = 58 x 3 + 46
We consider the new divisor 58 and the new remainder 46,and apply the division lemma to get
58 = 46 x 1 + 12
We consider the new divisor 46 and the new remainder 12,and apply the division lemma to get
46 = 12 x 3 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 776 and 498 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(46,12) = HCF(58,46) = HCF(220,58) = HCF(278,220) = HCF(498,278) = HCF(776,498) .
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Frequently Asked Questions on HCF of 776, 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 776, 498?
Answer: HCF of 776, 498 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 776, 498 using Euclid's Algorithm?
Answer: For arbitrary numbers 776, 498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.