Highest Common Factor of 354, 665, 353 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, 665, 353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 665, 353 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, 665, 353 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, 665, 353 is 1.
HCF(354, 665, 353) = 1
HCF of 354, 665, 353 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, 665, 353 is 1.
Highest Common Factor of 354,665,353 is 1
Step 1: Since 665 > 354, we apply the division lemma to 665 and 354, to get
665 = 354 x 1 + 311
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 311 and 354, to get
354 = 311 x 1 + 43
Step 3: We consider the new divisor 311 and the new remainder 43, and apply the division lemma to get
311 = 43 x 7 + 10
We consider the new divisor 43 and the new remainder 10,and apply the division lemma to get
43 = 10 x 4 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 354 and 665 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(43,10) = HCF(311,43) = HCF(354,311) = HCF(665,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 353 > 1, we apply the division lemma to 353 and 1, to get
353 = 1 x 353 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 353 is 1
Notice that 1 = HCF(353,1) .
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Frequently Asked Questions on HCF of 354, 665, 353 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, 665, 353?
Answer: HCF of 354, 665, 353 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 665, 353 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 665, 353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
