Highest Common Factor of 56, 364, 342, 221 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 56, 364, 342, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 56, 364, 342, 221 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 56, 364, 342, 221 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 56, 364, 342, 221 is 1.
HCF(56, 364, 342, 221) = 1
HCF of 56, 364, 342, 221 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 56, 364, 342, 221 is 1.
Highest Common Factor of 56,364,342,221 is 1
Step 1: Since 364 > 56, we apply the division lemma to 364 and 56, to get
364 = 56 x 6 + 28
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 28 and 56, to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 56 and 364 is 28
Notice that 28 = HCF(56,28) = HCF(364,56) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 28, we apply the division lemma to 342 and 28, to get
342 = 28 x 12 + 6
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 6 and 28, to get
28 = 6 x 4 + 4
Step 3: 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 28 and 342 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(342,28) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 221 > 2, we apply the division lemma to 221 and 2, to get
221 = 2 x 110 + 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 221 is 1
Notice that 1 = HCF(2,1) = HCF(221,2) .
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Frequently Asked Questions on HCF of 56, 364, 342, 221 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 56, 364, 342, 221?
Answer: HCF of 56, 364, 342, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 56, 364, 342, 221 using Euclid's Algorithm?
Answer: For arbitrary numbers 56, 364, 342, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.