Highest Common Factor of 878, 640, 411 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 878, 640, 411 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 878, 640, 411 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 878, 640, 411 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 878, 640, 411 is 1.
HCF(878, 640, 411) = 1
HCF of 878, 640, 411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 878, 640, 411 is 1.
Highest Common Factor of 878,640,411 is 1
Step 1: Since 878 > 640, we apply the division lemma to 878 and 640, to get
878 = 640 x 1 + 238
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 238 and 640, to get
640 = 238 x 2 + 164
Step 3: We consider the new divisor 238 and the new remainder 164, and apply the division lemma to get
238 = 164 x 1 + 74
We consider the new divisor 164 and the new remainder 74,and apply the division lemma to get
164 = 74 x 2 + 16
We consider the new divisor 74 and the new remainder 16,and apply the division lemma to get
74 = 16 x 4 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 878 and 640 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(74,16) = HCF(164,74) = HCF(238,164) = HCF(640,238) = HCF(878,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 2, we apply the division lemma to 411 and 2, to get
411 = 2 x 205 + 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 411 is 1
Notice that 1 = HCF(2,1) = HCF(411,2) .
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Frequently Asked Questions on HCF of 878, 640, 411 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 878, 640, 411?
Answer: HCF of 878, 640, 411 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 878, 640, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 878, 640, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.