Highest Common Factor of 971, 807, 342 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 971, 807, 342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 971, 807, 342 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 971, 807, 342 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 971, 807, 342 is 1.
HCF(971, 807, 342) = 1
HCF of 971, 807, 342 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 971, 807, 342 is 1.
Highest Common Factor of 971,807,342 is 1
Step 1: Since 971 > 807, we apply the division lemma to 971 and 807, to get
971 = 807 x 1 + 164
Step 2: Since the reminder 807 ≠ 0, we apply division lemma to 164 and 807, to get
807 = 164 x 4 + 151
Step 3: We consider the new divisor 164 and the new remainder 151, and apply the division lemma to get
164 = 151 x 1 + 13
We consider the new divisor 151 and the new remainder 13,and apply the division lemma to get
151 = 13 x 11 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 971 and 807 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(151,13) = HCF(164,151) = HCF(807,164) = HCF(971,807) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get
342 = 1 x 342 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1
Notice that 1 = HCF(342,1) .
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Frequently Asked Questions on HCF of 971, 807, 342 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 971, 807, 342?
Answer: HCF of 971, 807, 342 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 971, 807, 342 using Euclid's Algorithm?
Answer: For arbitrary numbers 971, 807, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
