Highest Common Factor of 357, 834, 194, 20 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 357, 834, 194, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 834, 194, 20 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 357, 834, 194, 20 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 357, 834, 194, 20 is 1.
HCF(357, 834, 194, 20) = 1
HCF of 357, 834, 194, 20 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 834, 194, 20 is 1.
Highest Common Factor of 357,834,194,20 is 1
Step 1: Since 834 > 357, we apply the division lemma to 834 and 357, to get
834 = 357 x 2 + 120
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 120 and 357, to get
357 = 120 x 2 + 117
Step 3: We consider the new divisor 120 and the new remainder 117, and apply the division lemma to get
120 = 117 x 1 + 3
We consider the new divisor 117 and the new remainder 3, and apply the division lemma to get
117 = 3 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 834 is 3
Notice that 3 = HCF(117,3) = HCF(120,117) = HCF(357,120) = HCF(834,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 194 > 3, we apply the division lemma to 194 and 3, to get
194 = 3 x 64 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 194 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(194,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1
Notice that 1 = HCF(20,1) .
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Frequently Asked Questions on HCF of 357, 834, 194, 20 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 357, 834, 194, 20?
Answer: HCF of 357, 834, 194, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 834, 194, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 834, 194, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.