Highest Common Factor of 696, 174, 460 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 696, 174, 460 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 174, 460 is 2 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 696, 174, 460 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 696, 174, 460 is 2.
HCF(696, 174, 460) = 2
HCF of 696, 174, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 696, 174, 460 is 2.
Highest Common Factor of 696,174,460 is 2
Step 1: Since 696 > 174, we apply the division lemma to 696 and 174, to get
696 = 174 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 174, the HCF of 696 and 174 is 174
Notice that 174 = HCF(696,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 174, we apply the division lemma to 460 and 174, to get
460 = 174 x 2 + 112
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 112 and 174, to get
174 = 112 x 1 + 62
Step 3: We consider the new divisor 112 and the new remainder 62, and apply the division lemma to get
112 = 62 x 1 + 50
We consider the new divisor 62 and the new remainder 50,and apply the division lemma to get
62 = 50 x 1 + 12
We consider the new divisor 50 and the new remainder 12,and apply the division lemma to get
50 = 12 x 4 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 174 and 460 is 2
Notice that 2 = HCF(12,2) = HCF(50,12) = HCF(62,50) = HCF(112,62) = HCF(174,112) = HCF(460,174) .
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Frequently Asked Questions on HCF of 696, 174, 460 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 696, 174, 460?
Answer: HCF of 696, 174, 460 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 174, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 174, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.