Highest Common Factor of 685, 998, 37 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 685, 998, 37 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 685, 998, 37 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 685, 998, 37 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 685, 998, 37 is 1.
HCF(685, 998, 37) = 1
HCF of 685, 998, 37 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 685, 998, 37 is 1.
Highest Common Factor of 685,998,37 is 1
Step 1: Since 998 > 685, we apply the division lemma to 998 and 685, to get
998 = 685 x 1 + 313
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 313 and 685, to get
685 = 313 x 2 + 59
Step 3: We consider the new divisor 313 and the new remainder 59, and apply the division lemma to get
313 = 59 x 5 + 18
We consider the new divisor 59 and the new remainder 18,and apply the division lemma to get
59 = 18 x 3 + 5
We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get
18 = 5 x 3 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 685 and 998 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(59,18) = HCF(313,59) = HCF(685,313) = HCF(998,685) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37 > 1, we apply the division lemma to 37 and 1, to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 37 is 1
Notice that 1 = HCF(37,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 685, 998, 37 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 685, 998, 37?
Answer: HCF of 685, 998, 37 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 685, 998, 37 using Euclid's Algorithm?
Answer: For arbitrary numbers 685, 998, 37 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
