Highest Common Factor of 834, 560, 37 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 834, 560, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 834, 560, 37 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 834, 560, 37 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 834, 560, 37 is 1.
HCF(834, 560, 37) = 1
HCF of 834, 560, 37 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 834, 560, 37 is 1.
Highest Common Factor of 834,560,37 is 1
Step 1: Since 834 > 560, we apply the division lemma to 834 and 560, to get
834 = 560 x 1 + 274
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 274 and 560, to get
560 = 274 x 2 + 12
Step 3: We consider the new divisor 274 and the new remainder 12, and apply the division lemma to get
274 = 12 x 22 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 834 and 560 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(274,12) = HCF(560,274) = HCF(834,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 2, we apply the division lemma to 37 and 2, to get
37 = 2 x 18 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 37 is 1
Notice that 1 = HCF(2,1) = HCF(37,2) .
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Frequently Asked Questions on HCF of 834, 560, 37 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 834, 560, 37?
Answer: HCF of 834, 560, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 834, 560, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 834, 560, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.