Highest Common Factor of 192, 320, 619 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, 320, 619 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 192, 320, 619 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, 320, 619 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, 320, 619 is 1.
HCF(192, 320, 619) = 1
HCF of 192, 320, 619 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, 320, 619 is 1.
Highest Common Factor of 192,320,619 is 1
Step 1: Since 320 > 192, we apply the division lemma to 320 and 192, to get
320 = 192 x 1 + 128
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 128 and 192, to get
192 = 128 x 1 + 64
Step 3: We consider the new divisor 128 and the new remainder 64, and apply the division lemma to get
128 = 64 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 64, the HCF of 192 and 320 is 64
Notice that 64 = HCF(128,64) = HCF(192,128) = HCF(320,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 619 > 64, we apply the division lemma to 619 and 64, to get
619 = 64 x 9 + 43
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 43 and 64, to get
64 = 43 x 1 + 21
Step 3: We consider the new divisor 43 and the new remainder 21, and apply the division lemma to get
43 = 21 x 2 + 1
We consider the new divisor 21 and the new remainder 1, and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 64 and 619 is 1
Notice that 1 = HCF(21,1) = HCF(43,21) = HCF(64,43) = HCF(619,64) .
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Frequently Asked Questions on HCF of 192, 320, 619 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, 320, 619?
Answer: HCF of 192, 320, 619 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 192, 320, 619 using Euclid's Algorithm?
Answer: For arbitrary numbers 192, 320, 619 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.