Highest Common Factor of 705, 997, 120 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 705, 997, 120 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 997, 120 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 705, 997, 120 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 705, 997, 120 is 1.
HCF(705, 997, 120) = 1
HCF of 705, 997, 120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 997, 120 is 1.
Highest Common Factor of 705,997,120 is 1
Step 1: Since 997 > 705, we apply the division lemma to 997 and 705, to get
997 = 705 x 1 + 292
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 292 and 705, to get
705 = 292 x 2 + 121
Step 3: We consider the new divisor 292 and the new remainder 121, and apply the division lemma to get
292 = 121 x 2 + 50
We consider the new divisor 121 and the new remainder 50,and apply the division lemma to get
121 = 50 x 2 + 21
We consider the new divisor 50 and the new remainder 21,and apply the division lemma to get
50 = 21 x 2 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 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 705 and 997 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(50,21) = HCF(121,50) = HCF(292,121) = HCF(705,292) = HCF(997,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 1, we apply the division lemma to 120 and 1, to get
120 = 1 x 120 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 120 is 1
Notice that 1 = HCF(120,1) .
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Frequently Asked Questions on HCF of 705, 997, 120 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 705, 997, 120?
Answer: HCF of 705, 997, 120 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 997, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 997, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.