Highest Common Factor of 354, 764, 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 354, 764, 343 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 764, 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 354, 764, 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 354, 764, 343 is 1.
HCF(354, 764, 343) = 1
HCF of 354, 764, 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 354, 764, 343 is 1.
Highest Common Factor of 354,764,343 is 1
Step 1: Since 764 > 354, we apply the division lemma to 764 and 354, to get
764 = 354 x 2 + 56
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 56 and 354, to get
354 = 56 x 6 + 18
Step 3: We consider the new divisor 56 and the new remainder 18, and apply the division lemma to get
56 = 18 x 3 + 2
We consider the new divisor 18 and the new remainder 2, and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 764 is 2
Notice that 2 = HCF(18,2) = HCF(56,18) = HCF(354,56) = HCF(764,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 343 > 2, we apply the division lemma to 343 and 2, to get
343 = 2 x 171 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 343 is 1
Notice that 1 = HCF(2,1) = HCF(343,2) .
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Frequently Asked Questions on HCF of 354, 764, 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 354, 764, 343?
Answer: HCF of 354, 764, 343 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 764, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 764, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.