Highest Common Factor of 690, 905, 345 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, 905, 345 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 905, 345 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 690, 905, 345 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, 905, 345 is 5.
HCF(690, 905, 345) = 5
HCF of 690, 905, 345 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, 905, 345 is 5.
Highest Common Factor of 690,905,345 is 5
Step 1: Since 905 > 690, we apply the division lemma to 905 and 690, to get
905 = 690 x 1 + 215
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 215 and 690, to get
690 = 215 x 3 + 45
Step 3: We consider the new divisor 215 and the new remainder 45, and apply the division lemma to get
215 = 45 x 4 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 690 and 905 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(215,45) = HCF(690,215) = HCF(905,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 345 > 5, we apply the division lemma to 345 and 5, to get
345 = 5 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 345 is 5
Notice that 5 = HCF(345,5) .
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Frequently Asked Questions on HCF of 690, 905, 345 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, 905, 345?
Answer: HCF of 690, 905, 345 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 905, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 905, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.