Highest Common Factor of 690, 369 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 690, 369 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 369 is 3 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 690, 369 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 690, 369 is 3.
HCF(690, 369) = 3
HCF of 690, 369 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 369 is 3.
Highest Common Factor of 690,369 is 3
Step 1: Since 690 > 369, we apply the division lemma to 690 and 369, to get
690 = 369 x 1 + 321
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 321 and 369, to get
369 = 321 x 1 + 48
Step 3: We consider the new divisor 321 and the new remainder 48, and apply the division lemma to get
321 = 48 x 6 + 33
We consider the new divisor 48 and the new remainder 33,and apply the division lemma to get
48 = 33 x 1 + 15
We consider the new divisor 33 and the new remainder 15,and apply the division lemma to get
33 = 15 x 2 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 690 and 369 is 3
Notice that 3 = HCF(15,3) = HCF(33,15) = HCF(48,33) = HCF(321,48) = HCF(369,321) = HCF(690,369) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 690, 369 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 690, 369?
Answer: HCF of 690, 369 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 369 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 369 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.