Highest Common Factor of 490, 3640, 6209 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, 3640, 6209 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 3640, 6209 is 7 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, 3640, 6209 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, 3640, 6209 is 7.
HCF(490, 3640, 6209) = 7
HCF of 490, 3640, 6209 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, 3640, 6209 is 7.
Highest Common Factor of 490,3640,6209 is 7
Step 1: Since 3640 > 490, we apply the division lemma to 3640 and 490, to get
3640 = 490 x 7 + 210
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 210 and 490, to get
490 = 210 x 2 + 70
Step 3: We consider the new divisor 210 and the new remainder 70, and apply the division lemma to get
210 = 70 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 490 and 3640 is 70
Notice that 70 = HCF(210,70) = HCF(490,210) = HCF(3640,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6209 > 70, we apply the division lemma to 6209 and 70, to get
6209 = 70 x 88 + 49
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 49 and 70, to get
70 = 49 x 1 + 21
Step 3: We consider the new divisor 49 and the new remainder 21, and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7, and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 70 and 6209 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(70,49) = HCF(6209,70) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 490, 3640, 6209 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, 3640, 6209?
Answer: HCF of 490, 3640, 6209 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 3640, 6209 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 3640, 6209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.