Highest Common Factor of 3737, 6780 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 3737, 6780 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3737, 6780 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 3737, 6780 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 3737, 6780 is 1.
HCF(3737, 6780) = 1
HCF of 3737, 6780 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3737, 6780 is 1.
Highest Common Factor of 3737,6780 is 1
Step 1: Since 6780 > 3737, we apply the division lemma to 6780 and 3737, to get
6780 = 3737 x 1 + 3043
Step 2: Since the reminder 3737 ≠ 0, we apply division lemma to 3043 and 3737, to get
3737 = 3043 x 1 + 694
Step 3: We consider the new divisor 3043 and the new remainder 694, and apply the division lemma to get
3043 = 694 x 4 + 267
We consider the new divisor 694 and the new remainder 267,and apply the division lemma to get
694 = 267 x 2 + 160
We consider the new divisor 267 and the new remainder 160,and apply the division lemma to get
267 = 160 x 1 + 107
We consider the new divisor 160 and the new remainder 107,and apply the division lemma to get
160 = 107 x 1 + 53
We consider the new divisor 107 and the new remainder 53,and apply the division lemma to get
107 = 53 x 2 + 1
We consider the new divisor 53 and the new remainder 1,and apply the division lemma to get
53 = 1 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3737 and 6780 is 1
Notice that 1 = HCF(53,1) = HCF(107,53) = HCF(160,107) = HCF(267,160) = HCF(694,267) = HCF(3043,694) = HCF(3737,3043) = HCF(6780,3737) .
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Frequently Asked Questions on HCF of 3737, 6780 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 3737, 6780?
Answer: HCF of 3737, 6780 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3737, 6780 using Euclid's Algorithm?
Answer: For arbitrary numbers 3737, 6780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.