Highest Common Factor of 5976, 9702 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 5976, 9702 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 5976, 9702 is 18 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 5976, 9702 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 5976, 9702 is 18.
HCF(5976, 9702) = 18
HCF of 5976, 9702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5976, 9702 is 18.
Highest Common Factor of 5976,9702 is 18
Step 1: Since 9702 > 5976, we apply the division lemma to 9702 and 5976, to get
9702 = 5976 x 1 + 3726
Step 2: Since the reminder 5976 ≠ 0, we apply division lemma to 3726 and 5976, to get
5976 = 3726 x 1 + 2250
Step 3: We consider the new divisor 3726 and the new remainder 2250, and apply the division lemma to get
3726 = 2250 x 1 + 1476
We consider the new divisor 2250 and the new remainder 1476,and apply the division lemma to get
2250 = 1476 x 1 + 774
We consider the new divisor 1476 and the new remainder 774,and apply the division lemma to get
1476 = 774 x 1 + 702
We consider the new divisor 774 and the new remainder 702,and apply the division lemma to get
774 = 702 x 1 + 72
We consider the new divisor 702 and the new remainder 72,and apply the division lemma to get
702 = 72 x 9 + 54
We consider the new divisor 72 and the new remainder 54,and apply the division lemma to get
72 = 54 x 1 + 18
We consider the new divisor 54 and the new remainder 18,and apply the division lemma to get
54 = 18 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 5976 and 9702 is 18
Notice that 18 = HCF(54,18) = HCF(72,54) = HCF(702,72) = HCF(774,702) = HCF(1476,774) = HCF(2250,1476) = HCF(3726,2250) = HCF(5976,3726) = HCF(9702,5976) .
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Frequently Asked Questions on HCF of 5976, 9702 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 5976, 9702?
Answer: HCF of 5976, 9702 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5976, 9702 using Euclid's Algorithm?
Answer: For arbitrary numbers 5976, 9702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.