Highest Common Factor of 208, 295, 709, 69 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 208, 295, 709, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 208, 295, 709, 69 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 208, 295, 709, 69 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 208, 295, 709, 69 is 1.
HCF(208, 295, 709, 69) = 1
HCF of 208, 295, 709, 69 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 208, 295, 709, 69 is 1.
Highest Common Factor of 208,295,709,69 is 1
Step 1: Since 295 > 208, we apply the division lemma to 295 and 208, to get
295 = 208 x 1 + 87
Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 87 and 208, to get
208 = 87 x 2 + 34
Step 3: We consider the new divisor 87 and the new remainder 34, and apply the division lemma to get
87 = 34 x 2 + 19
We consider the new divisor 34 and the new remainder 19,and apply the division lemma to get
34 = 19 x 1 + 15
We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get
19 = 15 x 1 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 208 and 295 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(34,19) = HCF(87,34) = HCF(208,87) = HCF(295,208) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 1, we apply the division lemma to 709 and 1, to get
709 = 1 x 709 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 709 is 1
Notice that 1 = HCF(709,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 1, we apply the division lemma to 69 and 1, to get
69 = 1 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69 is 1
Notice that 1 = HCF(69,1) .
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Frequently Asked Questions on HCF of 208, 295, 709, 69 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 208, 295, 709, 69?
Answer: HCF of 208, 295, 709, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 208, 295, 709, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 208, 295, 709, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
