Highest Common Factor of 400, 260, 211 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 400, 260, 211 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 260, 211 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 400, 260, 211 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 400, 260, 211 is 1.
HCF(400, 260, 211) = 1
HCF of 400, 260, 211 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 260, 211 is 1.
Highest Common Factor of 400,260,211 is 1
Step 1: Since 400 > 260, we apply the division lemma to 400 and 260, to get
400 = 260 x 1 + 140
Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 140 and 260, to get
260 = 140 x 1 + 120
Step 3: We consider the new divisor 140 and the new remainder 120, and apply the division lemma to get
140 = 120 x 1 + 20
We consider the new divisor 120 and the new remainder 20, and apply the division lemma to get
120 = 20 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 400 and 260 is 20
Notice that 20 = HCF(120,20) = HCF(140,120) = HCF(260,140) = HCF(400,260) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 211 > 20, we apply the division lemma to 211 and 20, to get
211 = 20 x 10 + 11
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 11 and 20, to get
20 = 11 x 1 + 9
Step 3: We consider the new divisor 11 and the new remainder 9, and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 20 and 211 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(211,20) .
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Frequently Asked Questions on HCF of 400, 260, 211 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 400, 260, 211?
Answer: HCF of 400, 260, 211 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 260, 211 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 260, 211 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.