Highest Common Factor of 998, 560, 621 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 998, 560, 621 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 560, 621 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 998, 560, 621 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 998, 560, 621 is 1.
HCF(998, 560, 621) = 1
HCF of 998, 560, 621 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 560, 621 is 1.
Highest Common Factor of 998,560,621 is 1
Step 1: Since 998 > 560, we apply the division lemma to 998 and 560, to get
998 = 560 x 1 + 438
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 438 and 560, to get
560 = 438 x 1 + 122
Step 3: We consider the new divisor 438 and the new remainder 122, and apply the division lemma to get
438 = 122 x 3 + 72
We consider the new divisor 122 and the new remainder 72,and apply the division lemma to get
122 = 72 x 1 + 50
We consider the new divisor 72 and the new remainder 50,and apply the division lemma to get
72 = 50 x 1 + 22
We consider the new divisor 50 and the new remainder 22,and apply the division lemma to get
50 = 22 x 2 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 560 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(72,50) = HCF(122,72) = HCF(438,122) = HCF(560,438) = HCF(998,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 621 > 2, we apply the division lemma to 621 and 2, to get
621 = 2 x 310 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 621 is 1
Notice that 1 = HCF(2,1) = HCF(621,2) .
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Frequently Asked Questions on HCF of 998, 560, 621 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 998, 560, 621?
Answer: HCF of 998, 560, 621 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 560, 621 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 560, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.