Highest Common Factor of 660, 422, 927 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 660, 422, 927 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 422, 927 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 660, 422, 927 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 660, 422, 927 is 1.
HCF(660, 422, 927) = 1
HCF of 660, 422, 927 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 422, 927 is 1.
Highest Common Factor of 660,422,927 is 1
Step 1: Since 660 > 422, we apply the division lemma to 660 and 422, to get
660 = 422 x 1 + 238
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 238 and 422, to get
422 = 238 x 1 + 184
Step 3: We consider the new divisor 238 and the new remainder 184, and apply the division lemma to get
238 = 184 x 1 + 54
We consider the new divisor 184 and the new remainder 54,and apply the division lemma to get
184 = 54 x 3 + 22
We consider the new divisor 54 and the new remainder 22,and apply the division lemma to get
54 = 22 x 2 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 660 and 422 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(184,54) = HCF(238,184) = HCF(422,238) = HCF(660,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 927 > 2, we apply the division lemma to 927 and 2, to get
927 = 2 x 463 + 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 927 is 1
Notice that 1 = HCF(2,1) = HCF(927,2) .
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Frequently Asked Questions on HCF of 660, 422, 927 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 660, 422, 927?
Answer: HCF of 660, 422, 927 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 422, 927 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 422, 927 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.