Highest Common Factor of 350, 600, 685 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 350, 600, 685 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 350, 600, 685 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 350, 600, 685 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 350, 600, 685 is 5.
HCF(350, 600, 685) = 5
HCF of 350, 600, 685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 350, 600, 685 is 5.
Highest Common Factor of 350,600,685 is 5
Step 1: Since 600 > 350, we apply the division lemma to 600 and 350, to get
600 = 350 x 1 + 250
Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 250 and 350, to get
350 = 250 x 1 + 100
Step 3: We consider the new divisor 250 and the new remainder 100, and apply the division lemma to get
250 = 100 x 2 + 50
We consider the new divisor 100 and the new remainder 50, and apply the division lemma to get
100 = 50 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 350 and 600 is 50
Notice that 50 = HCF(100,50) = HCF(250,100) = HCF(350,250) = HCF(600,350) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 50, we apply the division lemma to 685 and 50, to get
685 = 50 x 13 + 35
Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 35 and 50, to get
50 = 35 x 1 + 15
Step 3: We consider the new divisor 35 and the new remainder 15, and apply the division lemma to get
35 = 15 x 2 + 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 50 and 685 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(50,35) = HCF(685,50) .
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Frequently Asked Questions on HCF of 350, 600, 685 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 350, 600, 685?
Answer: HCF of 350, 600, 685 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 350, 600, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 350, 600, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.