Highest Common Factor of 67, 109, 343 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 67, 109, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 67, 109, 343 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 67, 109, 343 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 67, 109, 343 is 1.
HCF(67, 109, 343) = 1
HCF of 67, 109, 343 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 67, 109, 343 is 1.
Highest Common Factor of 67,109,343 is 1
Step 1: Since 109 > 67, we apply the division lemma to 109 and 67, to get
109 = 67 x 1 + 42
Step 2: Since the reminder 67 ≠ 0, we apply division lemma to 42 and 67, to get
67 = 42 x 1 + 25
Step 3: We consider the new divisor 42 and the new remainder 25, and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 67 and 109 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(67,42) = HCF(109,67) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 343 > 1, we apply the division lemma to 343 and 1, to get
343 = 1 x 343 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 343 is 1
Notice that 1 = HCF(343,1) .
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Frequently Asked Questions on HCF of 67, 109, 343 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 67, 109, 343?
Answer: HCF of 67, 109, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 67, 109, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 67, 109, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.