Highest Common Factor of 209, 792, 514, 80 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 209, 792, 514, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 209, 792, 514, 80 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 209, 792, 514, 80 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 209, 792, 514, 80 is 1.
HCF(209, 792, 514, 80) = 1
HCF of 209, 792, 514, 80 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 209, 792, 514, 80 is 1.
Highest Common Factor of 209,792,514,80 is 1
Step 1: Since 792 > 209, we apply the division lemma to 792 and 209, to get
792 = 209 x 3 + 165
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 165 and 209, to get
209 = 165 x 1 + 44
Step 3: We consider the new divisor 165 and the new remainder 44, and apply the division lemma to get
165 = 44 x 3 + 33
We consider the new divisor 44 and the new remainder 33,and apply the division lemma to get
44 = 33 x 1 + 11
We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 209 and 792 is 11
Notice that 11 = HCF(33,11) = HCF(44,33) = HCF(165,44) = HCF(209,165) = HCF(792,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 11, we apply the division lemma to 514 and 11, to get
514 = 11 x 46 + 8
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get
11 = 8 x 1 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 11 and 514 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(514,11) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get
80 = 1 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1
Notice that 1 = HCF(80,1) .
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Frequently Asked Questions on HCF of 209, 792, 514, 80 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 209, 792, 514, 80?
Answer: HCF of 209, 792, 514, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 209, 792, 514, 80 using Euclid's Algorithm?
Answer: For arbitrary numbers 209, 792, 514, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.