Highest Common Factor of 122, 854, 338 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 122, 854, 338 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 122, 854, 338 is 2 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 122, 854, 338 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 122, 854, 338 is 2.
HCF(122, 854, 338) = 2
HCF of 122, 854, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 122, 854, 338 is 2.
Highest Common Factor of 122,854,338 is 2
Step 1: Since 854 > 122, we apply the division lemma to 854 and 122, to get
854 = 122 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 122, the HCF of 122 and 854 is 122
Notice that 122 = HCF(854,122) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 122, we apply the division lemma to 338 and 122, to get
338 = 122 x 2 + 94
Step 2: Since the reminder 122 ≠ 0, we apply division lemma to 94 and 122, to get
122 = 94 x 1 + 28
Step 3: We consider the new divisor 94 and the new remainder 28, and apply the division lemma to get
94 = 28 x 3 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 122 and 338 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(94,28) = HCF(122,94) = HCF(338,122) .
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Frequently Asked Questions on HCF of 122, 854, 338 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 122, 854, 338?
Answer: HCF of 122, 854, 338 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 122, 854, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 122, 854, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.