Highest Common Factor of 651, 405, 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 651, 405, 124 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 651, 405, 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 651, 405, 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 651, 405, 124 is 1.
HCF(651, 405, 124) = 1
HCF of 651, 405, 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 651, 405, 124 is 1.
Highest Common Factor of 651,405,124 is 1
Step 1: Since 651 > 405, we apply the division lemma to 651 and 405, to get
651 = 405 x 1 + 246
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 246 and 405, to get
405 = 246 x 1 + 159
Step 3: We consider the new divisor 246 and the new remainder 159, and apply the division lemma to get
246 = 159 x 1 + 87
We consider the new divisor 159 and the new remainder 87,and apply the division lemma to get
159 = 87 x 1 + 72
We consider the new divisor 87 and the new remainder 72,and apply the division lemma to get
87 = 72 x 1 + 15
We consider the new divisor 72 and the new remainder 15,and apply the division lemma to get
72 = 15 x 4 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 651 and 405 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(72,15) = HCF(87,72) = HCF(159,87) = HCF(246,159) = HCF(405,246) = HCF(651,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 124 > 3, we apply the division lemma to 124 and 3, to get
124 = 3 x 41 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 124 is 1
Notice that 1 = HCF(3,1) = HCF(124,3) .
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Frequently Asked Questions on HCF of 651, 405, 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 651, 405, 124?
Answer: HCF of 651, 405, 124 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 651, 405, 124 using Euclid's Algorithm?
Answer: For arbitrary numbers 651, 405, 124 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.