Highest Common Factor of 634, 782, 13 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 634, 782, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 634, 782, 13 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 634, 782, 13 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 634, 782, 13 is 1.
HCF(634, 782, 13) = 1
HCF of 634, 782, 13 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 634, 782, 13 is 1.
Highest Common Factor of 634,782,13 is 1
Step 1: Since 782 > 634, we apply the division lemma to 782 and 634, to get
782 = 634 x 1 + 148
Step 2: Since the reminder 634 ≠ 0, we apply division lemma to 148 and 634, to get
634 = 148 x 4 + 42
Step 3: We consider the new divisor 148 and the new remainder 42, and apply the division lemma to get
148 = 42 x 3 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 634 and 782 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(148,42) = HCF(634,148) = HCF(782,634) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13 > 2, we apply the division lemma to 13 and 2, to get
13 = 2 x 6 + 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 13 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) .
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Frequently Asked Questions on HCF of 634, 782, 13 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 634, 782, 13?
Answer: HCF of 634, 782, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 634, 782, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 634, 782, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.