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 621, 341, 354, 411 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 621, 341, 354, 411 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 621, 341, 354, 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 621, 341, 354, 411 is 1.
HCF(621, 341, 354, 411) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 621, 341, 354, 411 is 1.
Step 1: Since 621 > 341, we apply the division lemma to 621 and 341, to get
621 = 341 x 1 + 280
Step 2: Since the reminder 341 ≠ 0, we apply division lemma to 280 and 341, to get
341 = 280 x 1 + 61
Step 3: We consider the new divisor 280 and the new remainder 61, and apply the division lemma to get
280 = 61 x 4 + 36
We consider the new divisor 61 and the new remainder 36,and apply the division lemma to get
61 = 36 x 1 + 25
We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get
36 = 25 x 1 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 621 and 341 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(61,36) = HCF(280,61) = HCF(341,280) = HCF(621,341) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get
354 = 1 x 354 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1
Notice that 1 = HCF(354,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 1, we apply the division lemma to 411 and 1, to get
411 = 1 x 411 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 411 is 1
Notice that 1 = HCF(411,1) .
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 621, 341, 354, 411?
Answer: HCF of 621, 341, 354, 411 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 621, 341, 354, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 621, 341, 354, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.