Highest Common Factor of 842, 228, 138, 61 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 842, 228, 138, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 842, 228, 138, 61 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 842, 228, 138, 61 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 842, 228, 138, 61 is 1.
HCF(842, 228, 138, 61) = 1
HCF of 842, 228, 138, 61 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 842, 228, 138, 61 is 1.
Highest Common Factor of 842,228,138,61 is 1
Step 1: Since 842 > 228, we apply the division lemma to 842 and 228, to get
842 = 228 x 3 + 158
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 158 and 228, to get
228 = 158 x 1 + 70
Step 3: We consider the new divisor 158 and the new remainder 70, and apply the division lemma to get
158 = 70 x 2 + 18
We consider the new divisor 70 and the new remainder 18,and apply the division lemma to get
70 = 18 x 3 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 842 and 228 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70,18) = HCF(158,70) = HCF(228,158) = HCF(842,228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 2, we apply the division lemma to 138 and 2, to get
138 = 2 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 138 is 2
Notice that 2 = HCF(138,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 2, we apply the division lemma to 61 and 2, to get
61 = 2 x 30 + 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 61 is 1
Notice that 1 = HCF(2,1) = HCF(61,2) .
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Frequently Asked Questions on HCF of 842, 228, 138, 61 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 842, 228, 138, 61?
Answer: HCF of 842, 228, 138, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 842, 228, 138, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 842, 228, 138, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.