Highest Common Factor of 341, 221, 222 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 341, 221, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 341, 221, 222 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 341, 221, 222 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 341, 221, 222 is 1.
HCF(341, 221, 222) = 1
HCF of 341, 221, 222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 341, 221, 222 is 1.
Highest Common Factor of 341,221,222 is 1
Step 1: Since 341 > 221, we apply the division lemma to 341 and 221, to get
341 = 221 x 1 + 120
Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 120 and 221, to get
221 = 120 x 1 + 101
Step 3: We consider the new divisor 120 and the new remainder 101, and apply the division lemma to get
120 = 101 x 1 + 19
We consider the new divisor 101 and the new remainder 19,and apply the division lemma to get
101 = 19 x 5 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 341 and 221 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(101,19) = HCF(120,101) = HCF(221,120) = HCF(341,221) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get
222 = 1 x 222 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1
Notice that 1 = HCF(222,1) .
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Frequently Asked Questions on HCF of 341, 221, 222 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 341, 221, 222?
Answer: HCF of 341, 221, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 341, 221, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 341, 221, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.