Highest Common Factor of 192, 661, 649 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 192, 661, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 192, 661, 649 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 192, 661, 649 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 192, 661, 649 is 1.
HCF(192, 661, 649) = 1
HCF of 192, 661, 649 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 192, 661, 649 is 1.
Highest Common Factor of 192,661,649 is 1
Step 1: Since 661 > 192, we apply the division lemma to 661 and 192, to get
661 = 192 x 3 + 85
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 85 and 192, to get
192 = 85 x 2 + 22
Step 3: We consider the new divisor 85 and the new remainder 22, and apply the division lemma to get
85 = 22 x 3 + 19
We consider the new divisor 22 and the new remainder 19,and apply the division lemma to get
22 = 19 x 1 + 3
We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get
19 = 3 x 6 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 192 and 661 is 1
Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(85,22) = HCF(192,85) = HCF(661,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 649 > 1, we apply the division lemma to 649 and 1, to get
649 = 1 x 649 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 649 is 1
Notice that 1 = HCF(649,1) .
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Frequently Asked Questions on HCF of 192, 661, 649 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 192, 661, 649?
Answer: HCF of 192, 661, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 192, 661, 649 using Euclid's Algorithm?
Answer: For arbitrary numbers 192, 661, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.