Highest Common Factor of 654, 8980 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, 8980 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 8980 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 654, 8980 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, 8980 is 2.
HCF(654, 8980) = 2
HCF of 654, 8980 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, 8980 is 2.
Highest Common Factor of 654,8980 is 2
Step 1: Since 8980 > 654, we apply the division lemma to 8980 and 654, to get
8980 = 654 x 13 + 478
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 478 and 654, to get
654 = 478 x 1 + 176
Step 3: We consider the new divisor 478 and the new remainder 176, and apply the division lemma to get
478 = 176 x 2 + 126
We consider the new divisor 176 and the new remainder 126,and apply the division lemma to get
176 = 126 x 1 + 50
We consider the new divisor 126 and the new remainder 50,and apply the division lemma to get
126 = 50 x 2 + 26
We consider the new divisor 50 and the new remainder 26,and apply the division lemma to get
50 = 26 x 1 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 654 and 8980 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(50,26) = HCF(126,50) = HCF(176,126) = HCF(478,176) = HCF(654,478) = HCF(8980,654) .
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Frequently Asked Questions on HCF of 654, 8980 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, 8980?
Answer: HCF of 654, 8980 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 8980 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 8980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
