Highest Common Factor of 663, 390, 296 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 663, 390, 296 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 390, 296 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 663, 390, 296 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 663, 390, 296 is 1.
HCF(663, 390, 296) = 1
HCF of 663, 390, 296 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 390, 296 is 1.
Highest Common Factor of 663,390,296 is 1
Step 1: Since 663 > 390, we apply the division lemma to 663 and 390, to get
663 = 390 x 1 + 273
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 273 and 390, to get
390 = 273 x 1 + 117
Step 3: We consider the new divisor 273 and the new remainder 117, and apply the division lemma to get
273 = 117 x 2 + 39
We consider the new divisor 117 and the new remainder 39, and apply the division lemma to get
117 = 39 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 663 and 390 is 39
Notice that 39 = HCF(117,39) = HCF(273,117) = HCF(390,273) = HCF(663,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 296 > 39, we apply the division lemma to 296 and 39, to get
296 = 39 x 7 + 23
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 23 and 39, to get
39 = 23 x 1 + 16
Step 3: We consider the new divisor 23 and the new remainder 16, and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 39 and 296 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(39,23) = HCF(296,39) .
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Frequently Asked Questions on HCF of 663, 390, 296 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 663, 390, 296?
Answer: HCF of 663, 390, 296 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 390, 296 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 390, 296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
