Highest Common Factor of 654, 6774 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, 6774 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 6774 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, 6774 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, 6774 is 6.
HCF(654, 6774) = 6
HCF of 654, 6774 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, 6774 is 6.
Highest Common Factor of 654,6774 is 6
Step 1: Since 6774 > 654, we apply the division lemma to 6774 and 654, to get
6774 = 654 x 10 + 234
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 234 and 654, to get
654 = 234 x 2 + 186
Step 3: We consider the new divisor 234 and the new remainder 186, and apply the division lemma to get
234 = 186 x 1 + 48
We consider the new divisor 186 and the new remainder 48,and apply the division lemma to get
186 = 48 x 3 + 42
We consider the new divisor 48 and the new remainder 42,and apply the division lemma to get
48 = 42 x 1 + 6
We consider the new divisor 42 and the new remainder 6,and apply the division lemma to get
42 = 6 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 654 and 6774 is 6
Notice that 6 = HCF(42,6) = HCF(48,42) = HCF(186,48) = HCF(234,186) = HCF(654,234) = HCF(6774,654) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 654, 6774 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, 6774?
Answer: HCF of 654, 6774 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 6774 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 6774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
