Highest Common Factor of 638, 705, 105, 877 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 638, 705, 105, 877 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 705, 105, 877 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 638, 705, 105, 877 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 638, 705, 105, 877 is 1.
HCF(638, 705, 105, 877) = 1
HCF of 638, 705, 105, 877 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 705, 105, 877 is 1.
Highest Common Factor of 638,705,105,877 is 1
Step 1: Since 705 > 638, we apply the division lemma to 705 and 638, to get
705 = 638 x 1 + 67
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 67 and 638, to get
638 = 67 x 9 + 35
Step 3: We consider the new divisor 67 and the new remainder 35, and apply the division lemma to get
67 = 35 x 1 + 32
We consider the new divisor 35 and the new remainder 32,and apply the division lemma to get
35 = 32 x 1 + 3
We consider the new divisor 32 and the new remainder 3,and apply the division lemma to get
32 = 3 x 10 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 638 and 705 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) = HCF(35,32) = HCF(67,35) = HCF(638,67) = HCF(705,638) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 877 > 1, we apply the division lemma to 877 and 1, to get
877 = 1 x 877 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 877 is 1
Notice that 1 = HCF(877,1) .
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Frequently Asked Questions on HCF of 638, 705, 105, 877 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 638, 705, 105, 877?
Answer: HCF of 638, 705, 105, 877 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 705, 105, 877 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 705, 105, 877 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.