Highest Common Factor of 8255, 9685, 38191 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 8255, 9685, 38191 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8255, 9685, 38191 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 8255, 9685, 38191 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 8255, 9685, 38191 is 1.
HCF(8255, 9685, 38191) = 1
HCF of 8255, 9685, 38191 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8255, 9685, 38191 is 1.
Highest Common Factor of 8255,9685,38191 is 1
Step 1: Since 9685 > 8255, we apply the division lemma to 9685 and 8255, to get
9685 = 8255 x 1 + 1430
Step 2: Since the reminder 8255 ≠ 0, we apply division lemma to 1430 and 8255, to get
8255 = 1430 x 5 + 1105
Step 3: We consider the new divisor 1430 and the new remainder 1105, and apply the division lemma to get
1430 = 1105 x 1 + 325
We consider the new divisor 1105 and the new remainder 325,and apply the division lemma to get
1105 = 325 x 3 + 130
We consider the new divisor 325 and the new remainder 130,and apply the division lemma to get
325 = 130 x 2 + 65
We consider the new divisor 130 and the new remainder 65,and apply the division lemma to get
130 = 65 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 8255 and 9685 is 65
Notice that 65 = HCF(130,65) = HCF(325,130) = HCF(1105,325) = HCF(1430,1105) = HCF(8255,1430) = HCF(9685,8255) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38191 > 65, we apply the division lemma to 38191 and 65, to get
38191 = 65 x 587 + 36
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 36 and 65, to get
65 = 36 x 1 + 29
Step 3: We consider the new divisor 36 and the new remainder 29, and apply the division lemma to get
36 = 29 x 1 + 7
We consider the new divisor 29 and the new remainder 7,and apply the division lemma to get
29 = 7 x 4 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 65 and 38191 is 1
Notice that 1 = HCF(7,1) = HCF(29,7) = HCF(36,29) = HCF(65,36) = HCF(38191,65) .
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Frequently Asked Questions on HCF of 8255, 9685, 38191 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 8255, 9685, 38191?
Answer: HCF of 8255, 9685, 38191 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8255, 9685, 38191 using Euclid's Algorithm?
Answer: For arbitrary numbers 8255, 9685, 38191 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.