Highest Common Factor of 340, 971, 116 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 340, 971, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 971, 116 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 340, 971, 116 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 340, 971, 116 is 1.
HCF(340, 971, 116) = 1
HCF of 340, 971, 116 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 971, 116 is 1.
Highest Common Factor of 340,971,116 is 1
Step 1: Since 971 > 340, we apply the division lemma to 971 and 340, to get
971 = 340 x 2 + 291
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 291 and 340, to get
340 = 291 x 1 + 49
Step 3: We consider the new divisor 291 and the new remainder 49, and apply the division lemma to get
291 = 49 x 5 + 46
We consider the new divisor 49 and the new remainder 46,and apply the division lemma to get
49 = 46 x 1 + 3
We consider the new divisor 46 and the new remainder 3,and apply the division lemma to get
46 = 3 x 15 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 340 and 971 is 1
Notice that 1 = HCF(3,1) = HCF(46,3) = HCF(49,46) = HCF(291,49) = HCF(340,291) = HCF(971,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 1, we apply the division lemma to 116 and 1, to get
116 = 1 x 116 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 116 is 1
Notice that 1 = HCF(116,1) .
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Frequently Asked Questions on HCF of 340, 971, 116 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 340, 971, 116?
Answer: HCF of 340, 971, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 971, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 971, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.