Highest Common Factor of 185, 6955, 1353 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 185, 6955, 1353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 185, 6955, 1353 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 185, 6955, 1353 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 185, 6955, 1353 is 1.
HCF(185, 6955, 1353) = 1
HCF of 185, 6955, 1353 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 185, 6955, 1353 is 1.
Highest Common Factor of 185,6955,1353 is 1
Step 1: Since 6955 > 185, we apply the division lemma to 6955 and 185, to get
6955 = 185 x 37 + 110
Step 2: Since the reminder 185 ≠ 0, we apply division lemma to 110 and 185, to get
185 = 110 x 1 + 75
Step 3: We consider the new divisor 110 and the new remainder 75, and apply the division lemma to get
110 = 75 x 1 + 35
We consider the new divisor 75 and the new remainder 35,and apply the division lemma to get
75 = 35 x 2 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 185 and 6955 is 5
Notice that 5 = HCF(35,5) = HCF(75,35) = HCF(110,75) = HCF(185,110) = HCF(6955,185) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1353 > 5, we apply the division lemma to 1353 and 5, to get
1353 = 5 x 270 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 5 and 1353 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(1353,5) .
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Frequently Asked Questions on HCF of 185, 6955, 1353 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 185, 6955, 1353?
Answer: HCF of 185, 6955, 1353 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 185, 6955, 1353 using Euclid's Algorithm?
Answer: For arbitrary numbers 185, 6955, 1353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.