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 340, 465, 682, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 465, 682, 685 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 340, 465, 682, 685 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 340, 465, 682, 685 is 1.
HCF(340, 465, 682, 685) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 465, 682, 685 is 1.
Step 1: Since 465 > 340, we apply the division lemma to 465 and 340, to get
465 = 340 x 1 + 125
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 125 and 340, to get
340 = 125 x 2 + 90
Step 3: We consider the new divisor 125 and the new remainder 90, and apply the division lemma to get
125 = 90 x 1 + 35
We consider the new divisor 90 and the new remainder 35,and apply the division lemma to get
90 = 35 x 2 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 340 and 465 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(90,35) = HCF(125,90) = HCF(340,125) = HCF(465,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 682 > 5, we apply the division lemma to 682 and 5, to get
682 = 5 x 136 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 682 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(682,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 1, we apply the division lemma to 685 and 1, to get
685 = 1 x 685 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 685 is 1
Notice that 1 = HCF(685,1) .
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 340, 465, 682, 685?
Answer: HCF of 340, 465, 682, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 465, 682, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 465, 682, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.