Highest Common Factor of 498, 874, 685 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 498, 874, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 874, 685 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 498, 874, 685 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 498, 874, 685 is 1.
HCF(498, 874, 685) = 1
HCF of 498, 874, 685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 874, 685 is 1.
Highest Common Factor of 498,874,685 is 1
Step 1: Since 874 > 498, we apply the division lemma to 874 and 498, to get
874 = 498 x 1 + 376
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 376 and 498, to get
498 = 376 x 1 + 122
Step 3: We consider the new divisor 376 and the new remainder 122, and apply the division lemma to get
376 = 122 x 3 + 10
We consider the new divisor 122 and the new remainder 10,and apply the division lemma to get
122 = 10 x 12 + 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 498 and 874 is 2
Notice that 2 = HCF(10,2) = HCF(122,10) = HCF(376,122) = HCF(498,376) = HCF(874,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 2, we apply the division lemma to 685 and 2, to get
685 = 2 x 342 + 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 685 is 1
Notice that 1 = HCF(2,1) = HCF(685,2) .
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Frequently Asked Questions on HCF of 498, 874, 685 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 498, 874, 685?
Answer: HCF of 498, 874, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 874, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 874, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.