Highest Common Factor of 705, 866, 388, 22 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, 866, 388, 22 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 866, 388, 22 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, 866, 388, 22 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, 866, 388, 22 is 1.
HCF(705, 866, 388, 22) = 1
HCF of 705, 866, 388, 22 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, 866, 388, 22 is 1.
Highest Common Factor of 705,866,388,22 is 1
Step 1: Since 866 > 705, we apply the division lemma to 866 and 705, to get
866 = 705 x 1 + 161
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 161 and 705, to get
705 = 161 x 4 + 61
Step 3: We consider the new divisor 161 and the new remainder 61, and apply the division lemma to get
161 = 61 x 2 + 39
We consider the new divisor 61 and the new remainder 39,and apply the division lemma to get
61 = 39 x 1 + 22
We consider the new divisor 39 and the new remainder 22,and apply the division lemma to get
39 = 22 x 1 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 705 and 866 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(39,22) = HCF(61,39) = HCF(161,61) = HCF(705,161) = HCF(866,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 388 > 1, we apply the division lemma to 388 and 1, to get
388 = 1 x 388 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 388 is 1
Notice that 1 = HCF(388,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 1, we apply the division lemma to 22 and 1, to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22 is 1
Notice that 1 = HCF(22,1) .
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Frequently Asked Questions on HCF of 705, 866, 388, 22 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, 866, 388, 22?
Answer: HCF of 705, 866, 388, 22 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 866, 388, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 866, 388, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.