Highest Common Factor of 187, 669, 659 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 187, 669, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 187, 669, 659 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 187, 669, 659 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 187, 669, 659 is 1.
HCF(187, 669, 659) = 1
HCF of 187, 669, 659 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 187, 669, 659 is 1.
Highest Common Factor of 187,669,659 is 1
Step 1: Since 669 > 187, we apply the division lemma to 669 and 187, to get
669 = 187 x 3 + 108
Step 2: Since the reminder 187 ≠ 0, we apply division lemma to 108 and 187, to get
187 = 108 x 1 + 79
Step 3: We consider the new divisor 108 and the new remainder 79, and apply the division lemma to get
108 = 79 x 1 + 29
We consider the new divisor 79 and the new remainder 29,and apply the division lemma to get
79 = 29 x 2 + 21
We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get
29 = 21 x 1 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 187 and 669 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(79,29) = HCF(108,79) = HCF(187,108) = HCF(669,187) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 659 > 1, we apply the division lemma to 659 and 1, to get
659 = 1 x 659 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 659 is 1
Notice that 1 = HCF(659,1) .
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Frequently Asked Questions on HCF of 187, 669, 659 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 187, 669, 659?
Answer: HCF of 187, 669, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 187, 669, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 187, 669, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.