Highest Common Factor of 654, 68 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, 68 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 68 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, 68 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, 68 is 2.
HCF(654, 68) = 2
HCF of 654, 68 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, 68 is 2.
Highest Common Factor of 654,68 is 2
Step 1: Since 654 > 68, we apply the division lemma to 654 and 68, to get
654 = 68 x 9 + 42
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 42 and 68, to get
68 = 42 x 1 + 26
Step 3: We consider the new divisor 42 and the new remainder 26, and apply the division lemma to get
42 = 26 x 1 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 654 and 68 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(68,42) = HCF(654,68) .
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Frequently Asked Questions on HCF of 654, 68 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, 68?
Answer: HCF of 654, 68 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.