Highest Common Factor of 705, 508, 307, 174 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, 508, 307, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 508, 307, 174 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, 508, 307, 174 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, 508, 307, 174 is 1.
HCF(705, 508, 307, 174) = 1
HCF of 705, 508, 307, 174 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, 508, 307, 174 is 1.
Highest Common Factor of 705,508,307,174 is 1
Step 1: Since 705 > 508, we apply the division lemma to 705 and 508, to get
705 = 508 x 1 + 197
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 197 and 508, to get
508 = 197 x 2 + 114
Step 3: We consider the new divisor 197 and the new remainder 114, and apply the division lemma to get
197 = 114 x 1 + 83
We consider the new divisor 114 and the new remainder 83,and apply the division lemma to get
114 = 83 x 1 + 31
We consider the new divisor 83 and the new remainder 31,and apply the division lemma to get
83 = 31 x 2 + 21
We consider the new divisor 31 and the new remainder 21,and apply the division lemma to get
31 = 21 x 1 + 10
We consider the new divisor 21 and the new remainder 10,and apply the division lemma to get
21 = 10 x 2 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 508 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(31,21) = HCF(83,31) = HCF(114,83) = HCF(197,114) = HCF(508,197) = HCF(705,508) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 307 > 1, we apply the division lemma to 307 and 1, to get
307 = 1 x 307 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 307 is 1
Notice that 1 = HCF(307,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 1, we apply the division lemma to 174 and 1, to get
174 = 1 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 174 is 1
Notice that 1 = HCF(174,1) .
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Frequently Asked Questions on HCF of 705, 508, 307, 174 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, 508, 307, 174?
Answer: HCF of 705, 508, 307, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 508, 307, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 508, 307, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.