Highest Common Factor of 2737, 1980, 32761 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 2737, 1980, 32761 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2737, 1980, 32761 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 2737, 1980, 32761 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 2737, 1980, 32761 is 1.
HCF(2737, 1980, 32761) = 1
HCF of 2737, 1980, 32761 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2737, 1980, 32761 is 1.
Highest Common Factor of 2737,1980,32761 is 1
Step 1: Since 2737 > 1980, we apply the division lemma to 2737 and 1980, to get
2737 = 1980 x 1 + 757
Step 2: Since the reminder 1980 ≠ 0, we apply division lemma to 757 and 1980, to get
1980 = 757 x 2 + 466
Step 3: We consider the new divisor 757 and the new remainder 466, and apply the division lemma to get
757 = 466 x 1 + 291
We consider the new divisor 466 and the new remainder 291,and apply the division lemma to get
466 = 291 x 1 + 175
We consider the new divisor 291 and the new remainder 175,and apply the division lemma to get
291 = 175 x 1 + 116
We consider the new divisor 175 and the new remainder 116,and apply the division lemma to get
175 = 116 x 1 + 59
We consider the new divisor 116 and the new remainder 59,and apply the division lemma to get
116 = 59 x 1 + 57
We consider the new divisor 59 and the new remainder 57,and apply the division lemma to get
59 = 57 x 1 + 2
We consider the new divisor 57 and the new remainder 2,and apply the division lemma to get
57 = 2 x 28 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2737 and 1980 is 1
Notice that 1 = HCF(2,1) = HCF(57,2) = HCF(59,57) = HCF(116,59) = HCF(175,116) = HCF(291,175) = HCF(466,291) = HCF(757,466) = HCF(1980,757) = HCF(2737,1980) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32761 > 1, we apply the division lemma to 32761 and 1, to get
32761 = 1 x 32761 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32761 is 1
Notice that 1 = HCF(32761,1) .
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Frequently Asked Questions on HCF of 2737, 1980, 32761 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 2737, 1980, 32761?
Answer: HCF of 2737, 1980, 32761 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2737, 1980, 32761 using Euclid's Algorithm?
Answer: For arbitrary numbers 2737, 1980, 32761 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
