Highest Common Factor of 610, 976, 934 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 610, 976, 934 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 976, 934 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 610, 976, 934 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 610, 976, 934 is 2.
HCF(610, 976, 934) = 2
HCF of 610, 976, 934 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 610, 976, 934 is 2.
Highest Common Factor of 610,976,934 is 2
Step 1: Since 976 > 610, we apply the division lemma to 976 and 610, to get
976 = 610 x 1 + 366
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 366 and 610, to get
610 = 366 x 1 + 244
Step 3: We consider the new divisor 366 and the new remainder 244, and apply the division lemma to get
366 = 244 x 1 + 122
We consider the new divisor 244 and the new remainder 122, and apply the division lemma to get
244 = 122 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 122, the HCF of 610 and 976 is 122
Notice that 122 = HCF(244,122) = HCF(366,244) = HCF(610,366) = HCF(976,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 934 > 122, we apply the division lemma to 934 and 122, to get
934 = 122 x 7 + 80
Step 2: Since the reminder 122 ≠ 0, we apply division lemma to 80 and 122, to get
122 = 80 x 1 + 42
Step 3: We consider the new divisor 80 and the new remainder 42, and apply the division lemma to get
80 = 42 x 1 + 38
We consider the new divisor 42 and the new remainder 38,and apply the division lemma to get
42 = 38 x 1 + 4
We consider the new divisor 38 and the new remainder 4,and apply the division lemma to get
38 = 4 x 9 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 122 and 934 is 2
Notice that 2 = HCF(4,2) = HCF(38,4) = HCF(42,38) = HCF(80,42) = HCF(122,80) = HCF(934,122) .
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Frequently Asked Questions on HCF of 610, 976, 934 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 610, 976, 934?
Answer: HCF of 610, 976, 934 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 976, 934 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 976, 934 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.