Highest Common Factor of 190, 692, 320 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 190, 692, 320 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 190, 692, 320 is 2 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 190, 692, 320 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 190, 692, 320 is 2.
HCF(190, 692, 320) = 2
HCF of 190, 692, 320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 190, 692, 320 is 2.
Highest Common Factor of 190,692,320 is 2
Step 1: Since 692 > 190, we apply the division lemma to 692 and 190, to get
692 = 190 x 3 + 122
Step 2: Since the reminder 190 ≠ 0, we apply division lemma to 122 and 190, to get
190 = 122 x 1 + 68
Step 3: We consider the new divisor 122 and the new remainder 68, and apply the division lemma to get
122 = 68 x 1 + 54
We consider the new divisor 68 and the new remainder 54,and apply the division lemma to get
68 = 54 x 1 + 14
We consider the new divisor 54 and the new remainder 14,and apply the division lemma to get
54 = 14 x 3 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 190 and 692 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(54,14) = HCF(68,54) = HCF(122,68) = HCF(190,122) = HCF(692,190) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 2, we apply the division lemma to 320 and 2, to get
320 = 2 x 160 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 320 is 2
Notice that 2 = HCF(320,2) .
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Frequently Asked Questions on HCF of 190, 692, 320 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 190, 692, 320?
Answer: HCF of 190, 692, 320 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 190, 692, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 190, 692, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.