Highest Common Factor of 421, 269 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 421, 269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 269 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 421, 269 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 421, 269 is 1.
HCF(421, 269) = 1
HCF of 421, 269 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 269 is 1.
Highest Common Factor of 421,269 is 1
Step 1: Since 421 > 269, we apply the division lemma to 421 and 269, to get
421 = 269 x 1 + 152
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 152 and 269, to get
269 = 152 x 1 + 117
Step 3: We consider the new divisor 152 and the new remainder 117, and apply the division lemma to get
152 = 117 x 1 + 35
We consider the new divisor 117 and the new remainder 35,and apply the division lemma to get
117 = 35 x 3 + 12
We consider the new divisor 35 and the new remainder 12,and apply the division lemma to get
35 = 12 x 2 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 269 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(35,12) = HCF(117,35) = HCF(152,117) = HCF(269,152) = HCF(421,269) .
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Frequently Asked Questions on HCF of 421, 269 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 421, 269?
Answer: HCF of 421, 269 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 269 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.