Highest Common Factor of 680, 175 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 680, 175 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 175 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 680, 175 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 680, 175 is 5.
HCF(680, 175) = 5
HCF of 680, 175 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 175 is 5.
Highest Common Factor of 680,175 is 5
Step 1: Since 680 > 175, we apply the division lemma to 680 and 175, to get
680 = 175 x 3 + 155
Step 2: Since the reminder 175 ≠ 0, we apply division lemma to 155 and 175, to get
175 = 155 x 1 + 20
Step 3: We consider the new divisor 155 and the new remainder 20, and apply the division lemma to get
155 = 20 x 7 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 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 680 and 175 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(155,20) = HCF(175,155) = HCF(680,175) .
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Frequently Asked Questions on HCF of 680, 175 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 680, 175?
Answer: HCF of 680, 175 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 175 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 175 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.