Highest Common Factor of 851, 690, 209 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 851, 690, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 851, 690, 209 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 851, 690, 209 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 851, 690, 209 is 1.
HCF(851, 690, 209) = 1
HCF of 851, 690, 209 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 851, 690, 209 is 1.
Highest Common Factor of 851,690,209 is 1
Step 1: Since 851 > 690, we apply the division lemma to 851 and 690, to get
851 = 690 x 1 + 161
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 161 and 690, to get
690 = 161 x 4 + 46
Step 3: We consider the new divisor 161 and the new remainder 46, and apply the division lemma to get
161 = 46 x 3 + 23
We consider the new divisor 46 and the new remainder 23, and apply the division lemma to get
46 = 23 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 851 and 690 is 23
Notice that 23 = HCF(46,23) = HCF(161,46) = HCF(690,161) = HCF(851,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 209 > 23, we apply the division lemma to 209 and 23, to get
209 = 23 x 9 + 2
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 2 and 23, to get
23 = 2 x 11 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 23 and 209 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(209,23) .
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Frequently Asked Questions on HCF of 851, 690, 209 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 851, 690, 209?
Answer: HCF of 851, 690, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 851, 690, 209 using Euclid's Algorithm?
Answer: For arbitrary numbers 851, 690, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
