Highest Common Factor of 298, 221, 219 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 298, 221, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 298, 221, 219 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 298, 221, 219 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 298, 221, 219 is 1.
HCF(298, 221, 219) = 1
HCF of 298, 221, 219 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 298, 221, 219 is 1.
Highest Common Factor of 298,221,219 is 1
Step 1: Since 298 > 221, we apply the division lemma to 298 and 221, to get
298 = 221 x 1 + 77
Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 77 and 221, to get
221 = 77 x 2 + 67
Step 3: We consider the new divisor 77 and the new remainder 67, and apply the division lemma to get
77 = 67 x 1 + 10
We consider the new divisor 67 and the new remainder 10,and apply the division lemma to get
67 = 10 x 6 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
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 298 and 221 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(67,10) = HCF(77,67) = HCF(221,77) = HCF(298,221) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 219 > 1, we apply the division lemma to 219 and 1, to get
219 = 1 x 219 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 219 is 1
Notice that 1 = HCF(219,1) .
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Frequently Asked Questions on HCF of 298, 221, 219 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 298, 221, 219?
Answer: HCF of 298, 221, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 298, 221, 219 using Euclid's Algorithm?
Answer: For arbitrary numbers 298, 221, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.