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 677, 556, 186, 444 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 677, 556, 186, 444 is 1 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 677, 556, 186, 444 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 677, 556, 186, 444 is 1.
HCF(677, 556, 186, 444) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 677, 556, 186, 444 is 1.
Step 1: Since 677 > 556, we apply the division lemma to 677 and 556, to get
677 = 556 x 1 + 121
Step 2: Since the reminder 556 ≠ 0, we apply division lemma to 121 and 556, to get
556 = 121 x 4 + 72
Step 3: We consider the new divisor 121 and the new remainder 72, and apply the division lemma to get
121 = 72 x 1 + 49
We consider the new divisor 72 and the new remainder 49,and apply the division lemma to get
72 = 49 x 1 + 23
We consider the new divisor 49 and the new remainder 23,and apply the division lemma to get
49 = 23 x 2 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 677 and 556 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(49,23) = HCF(72,49) = HCF(121,72) = HCF(556,121) = HCF(677,556) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 186 > 1, we apply the division lemma to 186 and 1, to get
186 = 1 x 186 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 186 is 1
Notice that 1 = HCF(186,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 444 > 1, we apply the division lemma to 444 and 1, to get
444 = 1 x 444 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 444 is 1
Notice that 1 = HCF(444,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 677, 556, 186, 444?
Answer: HCF of 677, 556, 186, 444 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 677, 556, 186, 444 using Euclid's Algorithm?
Answer: For arbitrary numbers 677, 556, 186, 444 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.