Highest Common Factor of 106, 342, 977, 12 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 106, 342, 977, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 106, 342, 977, 12 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 106, 342, 977, 12 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 106, 342, 977, 12 is 1.
HCF(106, 342, 977, 12) = 1
HCF of 106, 342, 977, 12 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 106, 342, 977, 12 is 1.
Highest Common Factor of 106,342,977,12 is 1
Step 1: Since 342 > 106, we apply the division lemma to 342 and 106, to get
342 = 106 x 3 + 24
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 24 and 106, to get
106 = 24 x 4 + 10
Step 3: We consider the new divisor 24 and the new remainder 10, and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 106 and 342 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(106,24) = HCF(342,106) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 2, we apply the division lemma to 977 and 2, to get
977 = 2 x 488 + 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 977 is 1
Notice that 1 = HCF(2,1) = HCF(977,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1
Notice that 1 = HCF(12,1) .
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Frequently Asked Questions on HCF of 106, 342, 977, 12 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 106, 342, 977, 12?
Answer: HCF of 106, 342, 977, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 106, 342, 977, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 106, 342, 977, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.