Highest Common Factor of 669, 196 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 669, 196 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 196 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 669, 196 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 669, 196 is 1.
HCF(669, 196) = 1
HCF of 669, 196 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 196 is 1.
Highest Common Factor of 669,196 is 1
Step 1: Since 669 > 196, we apply the division lemma to 669 and 196, to get
669 = 196 x 3 + 81
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 81 and 196, to get
196 = 81 x 2 + 34
Step 3: We consider the new divisor 81 and the new remainder 34, and apply the division lemma to get
81 = 34 x 2 + 13
We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get
34 = 13 x 2 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 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 669 and 196 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(81,34) = HCF(196,81) = HCF(669,196) .
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Frequently Asked Questions on HCF of 669, 196 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 669, 196?
Answer: HCF of 669, 196 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 196 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.