Highest Common Factor of 305, 690 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 305, 690 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 305, 690 is 5 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 305, 690 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 305, 690 is 5.
HCF(305, 690) = 5
HCF of 305, 690 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 305, 690 is 5.
Highest Common Factor of 305,690 is 5
Step 1: Since 690 > 305, we apply the division lemma to 690 and 305, to get
690 = 305 x 2 + 80
Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 80 and 305, to get
305 = 80 x 3 + 65
Step 3: We consider the new divisor 80 and the new remainder 65, and apply the division lemma to get
80 = 65 x 1 + 15
We consider the new divisor 65 and the new remainder 15,and apply the division lemma to get
65 = 15 x 4 + 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 305 and 690 is 5
Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(80,65) = HCF(305,80) = HCF(690,305) .
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Frequently Asked Questions on HCF of 305, 690 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 305, 690?
Answer: HCF of 305, 690 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 305, 690 using Euclid's Algorithm?
Answer: For arbitrary numbers 305, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.