Highest Common Factor of 410, 621, 974 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 410, 621, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 621, 974 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 410, 621, 974 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 410, 621, 974 is 1.
HCF(410, 621, 974) = 1
HCF of 410, 621, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 621, 974 is 1.
Highest Common Factor of 410,621,974 is 1
Step 1: Since 621 > 410, we apply the division lemma to 621 and 410, to get
621 = 410 x 1 + 211
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 211 and 410, to get
410 = 211 x 1 + 199
Step 3: We consider the new divisor 211 and the new remainder 199, and apply the division lemma to get
211 = 199 x 1 + 12
We consider the new divisor 199 and the new remainder 12,and apply the division lemma to get
199 = 12 x 16 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 410 and 621 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(199,12) = HCF(211,199) = HCF(410,211) = HCF(621,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 1, we apply the division lemma to 974 and 1, to get
974 = 1 x 974 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 974 is 1
Notice that 1 = HCF(974,1) .
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Frequently Asked Questions on HCF of 410, 621, 974 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 410, 621, 974?
Answer: HCF of 410, 621, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 621, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 621, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.