Highest Common Factor of 705, 311, 874 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 705, 311, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 311, 874 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 705, 311, 874 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 705, 311, 874 is 1.
HCF(705, 311, 874) = 1
HCF of 705, 311, 874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 311, 874 is 1.
Highest Common Factor of 705,311,874 is 1
Step 1: Since 705 > 311, we apply the division lemma to 705 and 311, to get
705 = 311 x 2 + 83
Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 83 and 311, to get
311 = 83 x 3 + 62
Step 3: We consider the new divisor 83 and the new remainder 62, and apply the division lemma to get
83 = 62 x 1 + 21
We consider the new divisor 62 and the new remainder 21,and apply the division lemma to get
62 = 21 x 2 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 311 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(62,21) = HCF(83,62) = HCF(311,83) = HCF(705,311) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 1, we apply the division lemma to 874 and 1, to get
874 = 1 x 874 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 874 is 1
Notice that 1 = HCF(874,1) .
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Frequently Asked Questions on HCF of 705, 311, 874 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 705, 311, 874?
Answer: HCF of 705, 311, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 311, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 311, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.