Highest Common Factor of 192, 696, 997 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, 696, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 192, 696, 997 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, 696, 997 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, 696, 997 is 1.
HCF(192, 696, 997) = 1
HCF of 192, 696, 997 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, 696, 997 is 1.
Highest Common Factor of 192,696,997 is 1
Step 1: Since 696 > 192, we apply the division lemma to 696 and 192, to get
696 = 192 x 3 + 120
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 120 and 192, to get
192 = 120 x 1 + 72
Step 3: We consider the new divisor 120 and the new remainder 72, and apply the division lemma to get
120 = 72 x 1 + 48
We consider the new divisor 72 and the new remainder 48,and apply the division lemma to get
72 = 48 x 1 + 24
We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 192 and 696 is 24
Notice that 24 = HCF(48,24) = HCF(72,48) = HCF(120,72) = HCF(192,120) = HCF(696,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 997 > 24, we apply the division lemma to 997 and 24, to get
997 = 24 x 41 + 13
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 13 and 24, to get
24 = 13 x 1 + 11
Step 3: We consider the new divisor 13 and the new remainder 11, and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 24 and 997 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(997,24) .
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Frequently Asked Questions on HCF of 192, 696, 997 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, 696, 997?
Answer: HCF of 192, 696, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 192, 696, 997 using Euclid's Algorithm?
Answer: For arbitrary numbers 192, 696, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
