Highest Common Factor of 490, 680 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 490, 680 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 680 is 10 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 490, 680 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 490, 680 is 10.
HCF(490, 680) = 10
HCF of 490, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 490, 680 is 10.
Highest Common Factor of 490,680 is 10
Step 1: Since 680 > 490, we apply the division lemma to 680 and 490, to get
680 = 490 x 1 + 190
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 190 and 490, to get
490 = 190 x 2 + 110
Step 3: We consider the new divisor 190 and the new remainder 110, and apply the division lemma to get
190 = 110 x 1 + 80
We consider the new divisor 110 and the new remainder 80,and apply the division lemma to get
110 = 80 x 1 + 30
We consider the new divisor 80 and the new remainder 30,and apply the division lemma to get
80 = 30 x 2 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 490 and 680 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(80,30) = HCF(110,80) = HCF(190,110) = HCF(490,190) = HCF(680,490) .
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Frequently Asked Questions on HCF of 490, 680 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 490, 680?
Answer: HCF of 490, 680 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.