Highest Common Factor of 687, 209, 42, 370 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 687, 209, 42, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 209, 42, 370 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 687, 209, 42, 370 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 687, 209, 42, 370 is 1.
HCF(687, 209, 42, 370) = 1
HCF of 687, 209, 42, 370 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 209, 42, 370 is 1.
Highest Common Factor of 687,209,42,370 is 1
Step 1: Since 687 > 209, we apply the division lemma to 687 and 209, to get
687 = 209 x 3 + 60
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 60 and 209, to get
209 = 60 x 3 + 29
Step 3: We consider the new divisor 60 and the new remainder 29, and apply the division lemma to get
60 = 29 x 2 + 2
We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get
29 = 2 x 14 + 1
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 687 and 209 is 1
Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(60,29) = HCF(209,60) = HCF(687,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 1, we apply the division lemma to 370 and 1, to get
370 = 1 x 370 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 370 is 1
Notice that 1 = HCF(370,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 687, 209, 42, 370 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 687, 209, 42, 370?
Answer: HCF of 687, 209, 42, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 209, 42, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 209, 42, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.