Highest Common Factor of 712, 199, 500, 364 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 712, 199, 500, 364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 199, 500, 364 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 712, 199, 500, 364 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 712, 199, 500, 364 is 1.
HCF(712, 199, 500, 364) = 1
HCF of 712, 199, 500, 364 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 199, 500, 364 is 1.
Highest Common Factor of 712,199,500,364 is 1
Step 1: Since 712 > 199, we apply the division lemma to 712 and 199, to get
712 = 199 x 3 + 115
Step 2: Since the reminder 199 ≠ 0, we apply division lemma to 115 and 199, to get
199 = 115 x 1 + 84
Step 3: We consider the new divisor 115 and the new remainder 84, and apply the division lemma to get
115 = 84 x 1 + 31
We consider the new divisor 84 and the new remainder 31,and apply the division lemma to get
84 = 31 x 2 + 22
We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get
31 = 22 x 1 + 9
We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get
22 = 9 x 2 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 712 and 199 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(84,31) = HCF(115,84) = HCF(199,115) = HCF(712,199) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 500 > 1, we apply the division lemma to 500 and 1, to get
500 = 1 x 500 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 500 is 1
Notice that 1 = HCF(500,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get
364 = 1 x 364 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1
Notice that 1 = HCF(364,1) .
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Frequently Asked Questions on HCF of 712, 199, 500, 364 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 712, 199, 500, 364?
Answer: HCF of 712, 199, 500, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 199, 500, 364 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 199, 500, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.