Highest Common Factor of 682, 784, 490 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, 784, 490 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 784, 490 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, 784, 490 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, 784, 490 is 2.
HCF(682, 784, 490) = 2
HCF of 682, 784, 490 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, 784, 490 is 2.
Highest Common Factor of 682,784,490 is 2
Step 1: Since 784 > 682, we apply the division lemma to 784 and 682, to get
784 = 682 x 1 + 102
Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 102 and 682, to get
682 = 102 x 6 + 70
Step 3: We consider the new divisor 102 and the new remainder 70, and apply the division lemma to get
102 = 70 x 1 + 32
We consider the new divisor 70 and the new remainder 32,and apply the division lemma to get
70 = 32 x 2 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 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 682 and 784 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(70,32) = HCF(102,70) = HCF(682,102) = HCF(784,682) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 490 > 2, we apply the division lemma to 490 and 2, to get
490 = 2 x 245 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 490 is 2
Notice that 2 = HCF(490,2) .
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Frequently Asked Questions on HCF of 682, 784, 490 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, 784, 490?
Answer: HCF of 682, 784, 490 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 784, 490 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 784, 490 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.