Highest Common Factor of 667, 455, 422 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 667, 455, 422 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 455, 422 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 667, 455, 422 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 667, 455, 422 is 1.
HCF(667, 455, 422) = 1
HCF of 667, 455, 422 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 455, 422 is 1.
Highest Common Factor of 667,455,422 is 1
Step 1: Since 667 > 455, we apply the division lemma to 667 and 455, to get
667 = 455 x 1 + 212
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 212 and 455, to get
455 = 212 x 2 + 31
Step 3: We consider the new divisor 212 and the new remainder 31, and apply the division lemma to get
212 = 31 x 6 + 26
We consider the new divisor 31 and the new remainder 26,and apply the division lemma to get
31 = 26 x 1 + 5
We consider the new divisor 26 and the new remainder 5,and apply the division lemma to get
26 = 5 x 5 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 455 is 1
Notice that 1 = HCF(5,1) = HCF(26,5) = HCF(31,26) = HCF(212,31) = HCF(455,212) = HCF(667,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 422 > 1, we apply the division lemma to 422 and 1, to get
422 = 1 x 422 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 422 is 1
Notice that 1 = HCF(422,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 667, 455, 422 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 667, 455, 422?
Answer: HCF of 667, 455, 422 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 455, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 455, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.