Highest Common Factor of 672, 704, 586 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 672, 704, 586 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 704, 586 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 672, 704, 586 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 672, 704, 586 is 2.
HCF(672, 704, 586) = 2
HCF of 672, 704, 586 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 704, 586 is 2.
Highest Common Factor of 672,704,586 is 2
Step 1: Since 704 > 672, we apply the division lemma to 704 and 672, to get
704 = 672 x 1 + 32
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 32 and 672, to get
672 = 32 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 672 and 704 is 32
Notice that 32 = HCF(672,32) = HCF(704,672) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 586 > 32, we apply the division lemma to 586 and 32, to get
586 = 32 x 18 + 10
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 10 and 32, to get
32 = 10 x 3 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 32 and 586 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(586,32) .
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Frequently Asked Questions on HCF of 672, 704, 586 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 672, 704, 586?
Answer: HCF of 672, 704, 586 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 704, 586 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 704, 586 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.