Highest Common Factor of 674, 460, 670, 588 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 674, 460, 670, 588 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 460, 670, 588 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 674, 460, 670, 588 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 674, 460, 670, 588 is 2.
HCF(674, 460, 670, 588) = 2
HCF of 674, 460, 670, 588 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 674, 460, 670, 588 is 2.
Highest Common Factor of 674,460,670,588 is 2
Step 1: Since 674 > 460, we apply the division lemma to 674 and 460, to get
674 = 460 x 1 + 214
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 214 and 460, to get
460 = 214 x 2 + 32
Step 3: We consider the new divisor 214 and the new remainder 32, and apply the division lemma to get
214 = 32 x 6 + 22
We consider the new divisor 32 and the new remainder 22,and apply the division lemma to get
32 = 22 x 1 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
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 674 and 460 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(214,32) = HCF(460,214) = HCF(674,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 670 > 2, we apply the division lemma to 670 and 2, to get
670 = 2 x 335 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 670 is 2
Notice that 2 = HCF(670,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 588 > 2, we apply the division lemma to 588 and 2, to get
588 = 2 x 294 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 588 is 2
Notice that 2 = HCF(588,2) .
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Frequently Asked Questions on HCF of 674, 460, 670, 588 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 674, 460, 670, 588?
Answer: HCF of 674, 460, 670, 588 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 460, 670, 588 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 460, 670, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.