Highest Common Factor of 654, 7008 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, 7008 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 7008 is 6 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, 7008 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, 7008 is 6.
HCF(654, 7008) = 6
HCF of 654, 7008 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, 7008 is 6.
Highest Common Factor of 654,7008 is 6
Step 1: Since 7008 > 654, we apply the division lemma to 7008 and 654, to get
7008 = 654 x 10 + 468
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 468 and 654, to get
654 = 468 x 1 + 186
Step 3: We consider the new divisor 468 and the new remainder 186, and apply the division lemma to get
468 = 186 x 2 + 96
We consider the new divisor 186 and the new remainder 96,and apply the division lemma to get
186 = 96 x 1 + 90
We consider the new divisor 96 and the new remainder 90,and apply the division lemma to get
96 = 90 x 1 + 6
We consider the new divisor 90 and the new remainder 6,and apply the division lemma to get
90 = 6 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 654 and 7008 is 6
Notice that 6 = HCF(90,6) = HCF(96,90) = HCF(186,96) = HCF(468,186) = HCF(654,468) = HCF(7008,654) .
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Frequently Asked Questions on HCF of 654, 7008 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, 7008?
Answer: HCF of 654, 7008 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 7008 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 7008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.