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 556, 200, 419, 293 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 556, 200, 419, 293 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 556, 200, 419, 293 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 556, 200, 419, 293 is 1.
HCF(556, 200, 419, 293) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 556, 200, 419, 293 is 1.
Step 1: Since 556 > 200, we apply the division lemma to 556 and 200, to get
556 = 200 x 2 + 156
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 156 and 200, to get
200 = 156 x 1 + 44
Step 3: We consider the new divisor 156 and the new remainder 44, and apply the division lemma to get
156 = 44 x 3 + 24
We consider the new divisor 44 and the new remainder 24,and apply the division lemma to get
44 = 24 x 1 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 556 and 200 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(156,44) = HCF(200,156) = HCF(556,200) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 419 > 4, we apply the division lemma to 419 and 4, to get
419 = 4 x 104 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 419 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(419,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 293 > 1, we apply the division lemma to 293 and 1, to get
293 = 1 x 293 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 293 is 1
Notice that 1 = HCF(293,1) .
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 556, 200, 419, 293?
Answer: HCF of 556, 200, 419, 293 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 556, 200, 419, 293 using Euclid's Algorithm?
Answer: For arbitrary numbers 556, 200, 419, 293 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.