Highest Common Factor of 663, 765, 124 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, 765, 124 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 765, 124 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, 765, 124 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, 765, 124 is 1.
HCF(663, 765, 124) = 1
HCF of 663, 765, 124 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, 765, 124 is 1.
Highest Common Factor of 663,765,124 is 1
Step 1: Since 765 > 663, we apply the division lemma to 765 and 663, to get
765 = 663 x 1 + 102
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 102 and 663, to get
663 = 102 x 6 + 51
Step 3: We consider the new divisor 102 and the new remainder 51, and apply the division lemma to get
102 = 51 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 51, the HCF of 663 and 765 is 51
Notice that 51 = HCF(102,51) = HCF(663,102) = HCF(765,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 124 > 51, we apply the division lemma to 124 and 51, to get
124 = 51 x 2 + 22
Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 22 and 51, to get
51 = 22 x 2 + 7
Step 3: We consider the new divisor 22 and the new remainder 7, and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 51 and 124 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(51,22) = HCF(124,51) .
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Frequently Asked Questions on HCF of 663, 765, 124 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, 765, 124?
Answer: HCF of 663, 765, 124 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 765, 124 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 765, 124 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.