Highest Common Factor of 680, 965, 985 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, 965, 985 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 965, 985 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, 965, 985 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, 965, 985 is 5.
HCF(680, 965, 985) = 5
HCF of 680, 965, 985 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, 965, 985 is 5.
Highest Common Factor of 680,965,985 is 5
Step 1: Since 965 > 680, we apply the division lemma to 965 and 680, to get
965 = 680 x 1 + 285
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 285 and 680, to get
680 = 285 x 2 + 110
Step 3: We consider the new divisor 285 and the new remainder 110, and apply the division lemma to get
285 = 110 x 2 + 65
We consider the new divisor 110 and the new remainder 65,and apply the division lemma to get
110 = 65 x 1 + 45
We consider the new divisor 65 and the new remainder 45,and apply the division lemma to get
65 = 45 x 1 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 680 and 965 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(65,45) = HCF(110,65) = HCF(285,110) = HCF(680,285) = HCF(965,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 985 > 5, we apply the division lemma to 985 and 5, to get
985 = 5 x 197 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 985 is 5
Notice that 5 = HCF(985,5) .
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Frequently Asked Questions on HCF of 680, 965, 985 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, 965, 985?
Answer: HCF of 680, 965, 985 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 965, 985 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 965, 985 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
