Highest Common Factor of 682, 974, 510 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, 974, 510 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 974, 510 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, 974, 510 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, 974, 510 is 2.
HCF(682, 974, 510) = 2
HCF of 682, 974, 510 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, 974, 510 is 2.
Highest Common Factor of 682,974,510 is 2
Step 1: Since 974 > 682, we apply the division lemma to 974 and 682, to get
974 = 682 x 1 + 292
Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 292 and 682, to get
682 = 292 x 2 + 98
Step 3: We consider the new divisor 292 and the new remainder 98, and apply the division lemma to get
292 = 98 x 2 + 96
We consider the new divisor 98 and the new remainder 96,and apply the division lemma to get
98 = 96 x 1 + 2
We consider the new divisor 96 and the new remainder 2,and apply the division lemma to get
96 = 2 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 682 and 974 is 2
Notice that 2 = HCF(96,2) = HCF(98,96) = HCF(292,98) = HCF(682,292) = HCF(974,682) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 510 > 2, we apply the division lemma to 510 and 2, to get
510 = 2 x 255 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 510 is 2
Notice that 2 = HCF(510,2) .
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Frequently Asked Questions on HCF of 682, 974, 510 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, 974, 510?
Answer: HCF of 682, 974, 510 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 974, 510 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 974, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.