Highest Common Factor of 610, 1937 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, 1937 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 1937 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 610, 1937 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, 1937 is 1.
HCF(610, 1937) = 1
HCF of 610, 1937 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, 1937 is 1.
Highest Common Factor of 610,1937 is 1
Step 1: Since 1937 > 610, we apply the division lemma to 1937 and 610, to get
1937 = 610 x 3 + 107
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 107 and 610, to get
610 = 107 x 5 + 75
Step 3: We consider the new divisor 107 and the new remainder 75, and apply the division lemma to get
107 = 75 x 1 + 32
We consider the new divisor 75 and the new remainder 32,and apply the division lemma to get
75 = 32 x 2 + 11
We consider the new divisor 32 and the new remainder 11,and apply the division lemma to get
32 = 11 x 2 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 610 and 1937 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(32,11) = HCF(75,32) = HCF(107,75) = HCF(610,107) = HCF(1937,610) .
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Frequently Asked Questions on HCF of 610, 1937 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, 1937?
Answer: HCF of 610, 1937 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 1937 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 1937 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
