Highest Common Factor of 422, 659, 109 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 422, 659, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 659, 109 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 422, 659, 109 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 422, 659, 109 is 1.
HCF(422, 659, 109) = 1
HCF of 422, 659, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 422, 659, 109 is 1.
Highest Common Factor of 422,659,109 is 1
Step 1: Since 659 > 422, we apply the division lemma to 659 and 422, to get
659 = 422 x 1 + 237
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 237 and 422, to get
422 = 237 x 1 + 185
Step 3: We consider the new divisor 237 and the new remainder 185, and apply the division lemma to get
237 = 185 x 1 + 52
We consider the new divisor 185 and the new remainder 52,and apply the division lemma to get
185 = 52 x 3 + 29
We consider the new divisor 52 and the new remainder 29,and apply the division lemma to get
52 = 29 x 1 + 23
We consider the new divisor 29 and the new remainder 23,and apply the division lemma to get
29 = 23 x 1 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 422 and 659 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(29,23) = HCF(52,29) = HCF(185,52) = HCF(237,185) = HCF(422,237) = HCF(659,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
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Frequently Asked Questions on HCF of 422, 659, 109 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 422, 659, 109?
Answer: HCF of 422, 659, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 659, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 659, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.