Highest Common Factor of 654, 984, 129 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 654, 984, 129 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 984, 129 is 3 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 654, 984, 129 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 654, 984, 129 is 3.
HCF(654, 984, 129) = 3
HCF of 654, 984, 129 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 984, 129 is 3.
Highest Common Factor of 654,984,129 is 3
Step 1: Since 984 > 654, we apply the division lemma to 984 and 654, to get
984 = 654 x 1 + 330
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 330 and 654, to get
654 = 330 x 1 + 324
Step 3: We consider the new divisor 330 and the new remainder 324, and apply the division lemma to get
330 = 324 x 1 + 6
We consider the new divisor 324 and the new remainder 6, and apply the division lemma to get
324 = 6 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 654 and 984 is 6
Notice that 6 = HCF(324,6) = HCF(330,324) = HCF(654,330) = HCF(984,654) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 6, we apply the division lemma to 129 and 6, to get
129 = 6 x 21 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 129 is 3
Notice that 3 = HCF(6,3) = HCF(129,6) .
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Frequently Asked Questions on HCF of 654, 984, 129 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 654, 984, 129?
Answer: HCF of 654, 984, 129 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 984, 129 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 984, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.