Highest Common Factor of 8402, 6981, 89506 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 8402, 6981, 89506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8402, 6981, 89506 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 8402, 6981, 89506 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 8402, 6981, 89506 is 1.
HCF(8402, 6981, 89506) = 1
HCF of 8402, 6981, 89506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8402, 6981, 89506 is 1.
Highest Common Factor of 8402,6981,89506 is 1
Step 1: Since 8402 > 6981, we apply the division lemma to 8402 and 6981, to get
8402 = 6981 x 1 + 1421
Step 2: Since the reminder 6981 ≠ 0, we apply division lemma to 1421 and 6981, to get
6981 = 1421 x 4 + 1297
Step 3: We consider the new divisor 1421 and the new remainder 1297, and apply the division lemma to get
1421 = 1297 x 1 + 124
We consider the new divisor 1297 and the new remainder 124,and apply the division lemma to get
1297 = 124 x 10 + 57
We consider the new divisor 124 and the new remainder 57,and apply the division lemma to get
124 = 57 x 2 + 10
We consider the new divisor 57 and the new remainder 10,and apply the division lemma to get
57 = 10 x 5 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 8402 and 6981 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(57,10) = HCF(124,57) = HCF(1297,124) = HCF(1421,1297) = HCF(6981,1421) = HCF(8402,6981) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 89506 > 1, we apply the division lemma to 89506 and 1, to get
89506 = 1 x 89506 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 89506 is 1
Notice that 1 = HCF(89506,1) .
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Frequently Asked Questions on HCF of 8402, 6981, 89506 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 8402, 6981, 89506?
Answer: HCF of 8402, 6981, 89506 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8402, 6981, 89506 using Euclid's Algorithm?
Answer: For arbitrary numbers 8402, 6981, 89506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.