Highest Common Factor of 666, 368, 355 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 666, 368, 355 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 666, 368, 355 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 666, 368, 355 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 666, 368, 355 is 1.
HCF(666, 368, 355) = 1
HCF of 666, 368, 355 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 666, 368, 355 is 1.
Highest Common Factor of 666,368,355 is 1
Step 1: Since 666 > 368, we apply the division lemma to 666 and 368, to get
666 = 368 x 1 + 298
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 298 and 368, to get
368 = 298 x 1 + 70
Step 3: We consider the new divisor 298 and the new remainder 70, and apply the division lemma to get
298 = 70 x 4 + 18
We consider the new divisor 70 and the new remainder 18,and apply the division lemma to get
70 = 18 x 3 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 666 and 368 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70,18) = HCF(298,70) = HCF(368,298) = HCF(666,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 355 > 2, we apply the division lemma to 355 and 2, to get
355 = 2 x 177 + 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 355 is 1
Notice that 1 = HCF(2,1) = HCF(355,2) .
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Frequently Asked Questions on HCF of 666, 368, 355 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 666, 368, 355?
Answer: HCF of 666, 368, 355 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 666, 368, 355 using Euclid's Algorithm?
Answer: For arbitrary numbers 666, 368, 355 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.