Highest Common Factor of 665, 353, 554 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 665, 353, 554 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 353, 554 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 665, 353, 554 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 665, 353, 554 is 1.
HCF(665, 353, 554) = 1
HCF of 665, 353, 554 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 353, 554 is 1.
Highest Common Factor of 665,353,554 is 1
Step 1: Since 665 > 353, we apply the division lemma to 665 and 353, to get
665 = 353 x 1 + 312
Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 312 and 353, to get
353 = 312 x 1 + 41
Step 3: We consider the new divisor 312 and the new remainder 41, and apply the division lemma to get
312 = 41 x 7 + 25
We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get
41 = 25 x 1 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 665 and 353 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(312,41) = HCF(353,312) = HCF(665,353) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 554 > 1, we apply the division lemma to 554 and 1, to get
554 = 1 x 554 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 554 is 1
Notice that 1 = HCF(554,1) .
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Frequently Asked Questions on HCF of 665, 353, 554 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 665, 353, 554?
Answer: HCF of 665, 353, 554 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 353, 554 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 353, 554 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.