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 710, 582, 674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 710, 582, 674 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 710, 582, 674 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 710, 582, 674 is 2.
HCF(710, 582, 674) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 710, 582, 674 is 2.
Step 1: Since 710 > 582, we apply the division lemma to 710 and 582, to get
710 = 582 x 1 + 128
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 128 and 582, to get
582 = 128 x 4 + 70
Step 3: We consider the new divisor 128 and the new remainder 70, and apply the division lemma to get
128 = 70 x 1 + 58
We consider the new divisor 70 and the new remainder 58,and apply the division lemma to get
70 = 58 x 1 + 12
We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 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 710 and 582 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(128,70) = HCF(582,128) = HCF(710,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 674 > 2, we apply the division lemma to 674 and 2, to get
674 = 2 x 337 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 674 is 2
Notice that 2 = HCF(674,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 710, 582, 674?
Answer: HCF of 710, 582, 674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 710, 582, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 710, 582, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.