Highest Common Factor of 837, 961, 51 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 837, 961, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 961, 51 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 837, 961, 51 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 837, 961, 51 is 1.
HCF(837, 961, 51) = 1
HCF of 837, 961, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 961, 51 is 1.
Highest Common Factor of 837,961,51 is 1
Step 1: Since 961 > 837, we apply the division lemma to 961 and 837, to get
961 = 837 x 1 + 124
Step 2: Since the reminder 837 ≠ 0, we apply division lemma to 124 and 837, to get
837 = 124 x 6 + 93
Step 3: We consider the new divisor 124 and the new remainder 93, and apply the division lemma to get
124 = 93 x 1 + 31
We consider the new divisor 93 and the new remainder 31, and apply the division lemma to get
93 = 31 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 837 and 961 is 31
Notice that 31 = HCF(93,31) = HCF(124,93) = HCF(837,124) = HCF(961,837) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 31, we apply the division lemma to 51 and 31, to get
51 = 31 x 1 + 20
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 20 and 31, to get
31 = 20 x 1 + 11
Step 3: We consider the new divisor 20 and the new remainder 11, and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 31 and 51 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(51,31) .
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Frequently Asked Questions on HCF of 837, 961, 51 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 837, 961, 51?
Answer: HCF of 837, 961, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 961, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 961, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.