Highest Common Factor of 343, 669, 505 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 343, 669, 505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 343, 669, 505 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 343, 669, 505 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 343, 669, 505 is 1.
HCF(343, 669, 505) = 1
HCF of 343, 669, 505 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 343, 669, 505 is 1.
Highest Common Factor of 343,669,505 is 1
Step 1: Since 669 > 343, we apply the division lemma to 669 and 343, to get
669 = 343 x 1 + 326
Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 326 and 343, to get
343 = 326 x 1 + 17
Step 3: We consider the new divisor 326 and the new remainder 17, and apply the division lemma to get
326 = 17 x 19 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 2
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 343 and 669 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(326,17) = HCF(343,326) = HCF(669,343) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 505 > 1, we apply the division lemma to 505 and 1, to get
505 = 1 x 505 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 505 is 1
Notice that 1 = HCF(505,1) .
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Frequently Asked Questions on HCF of 343, 669, 505 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 343, 669, 505?
Answer: HCF of 343, 669, 505 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 343, 669, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 343, 669, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.