Highest Common Factor of 678, 552, 411 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 678, 552, 411 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 552, 411 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 678, 552, 411 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 678, 552, 411 is 3.
HCF(678, 552, 411) = 3
HCF of 678, 552, 411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 552, 411 is 3.
Highest Common Factor of 678,552,411 is 3
Step 1: Since 678 > 552, we apply the division lemma to 678 and 552, to get
678 = 552 x 1 + 126
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 126 and 552, to get
552 = 126 x 4 + 48
Step 3: We consider the new divisor 126 and the new remainder 48, and apply the division lemma to get
126 = 48 x 2 + 30
We consider the new divisor 48 and the new remainder 30,and apply the division lemma to get
48 = 30 x 1 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 678 and 552 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(48,30) = HCF(126,48) = HCF(552,126) = HCF(678,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 6, we apply the division lemma to 411 and 6, to get
411 = 6 x 68 + 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 411 is 3
Notice that 3 = HCF(6,3) = HCF(411,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 678, 552, 411 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 678, 552, 411?
Answer: HCF of 678, 552, 411 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 552, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 552, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.