Highest Common Factor of 6710, 9776, 53872 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 6710, 9776, 53872 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6710, 9776, 53872 is 2 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 6710, 9776, 53872 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 6710, 9776, 53872 is 2.
HCF(6710, 9776, 53872) = 2
HCF of 6710, 9776, 53872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6710, 9776, 53872 is 2.
Highest Common Factor of 6710,9776,53872 is 2
Step 1: Since 9776 > 6710, we apply the division lemma to 9776 and 6710, to get
9776 = 6710 x 1 + 3066
Step 2: Since the reminder 6710 ≠ 0, we apply division lemma to 3066 and 6710, to get
6710 = 3066 x 2 + 578
Step 3: We consider the new divisor 3066 and the new remainder 578, and apply the division lemma to get
3066 = 578 x 5 + 176
We consider the new divisor 578 and the new remainder 176,and apply the division lemma to get
578 = 176 x 3 + 50
We consider the new divisor 176 and the new remainder 50,and apply the division lemma to get
176 = 50 x 3 + 26
We consider the new divisor 50 and the new remainder 26,and apply the division lemma to get
50 = 26 x 1 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6710 and 9776 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(50,26) = HCF(176,50) = HCF(578,176) = HCF(3066,578) = HCF(6710,3066) = HCF(9776,6710) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53872 > 2, we apply the division lemma to 53872 and 2, to get
53872 = 2 x 26936 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 53872 is 2
Notice that 2 = HCF(53872,2) .
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Frequently Asked Questions on HCF of 6710, 9776, 53872 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 6710, 9776, 53872?
Answer: HCF of 6710, 9776, 53872 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6710, 9776, 53872 using Euclid's Algorithm?
Answer: For arbitrary numbers 6710, 9776, 53872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.