Highest Common Factor of 687, 945, 591 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 687, 945, 591 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 945, 591 is 3 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 687, 945, 591 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 687, 945, 591 is 3.
HCF(687, 945, 591) = 3
HCF of 687, 945, 591 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 945, 591 is 3.
Highest Common Factor of 687,945,591 is 3
Step 1: Since 945 > 687, we apply the division lemma to 945 and 687, to get
945 = 687 x 1 + 258
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 258 and 687, to get
687 = 258 x 2 + 171
Step 3: We consider the new divisor 258 and the new remainder 171, and apply the division lemma to get
258 = 171 x 1 + 87
We consider the new divisor 171 and the new remainder 87,and apply the division lemma to get
171 = 87 x 1 + 84
We consider the new divisor 87 and the new remainder 84,and apply the division lemma to get
87 = 84 x 1 + 3
We consider the new divisor 84 and the new remainder 3,and apply the division lemma to get
84 = 3 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 687 and 945 is 3
Notice that 3 = HCF(84,3) = HCF(87,84) = HCF(171,87) = HCF(258,171) = HCF(687,258) = HCF(945,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 591 > 3, we apply the division lemma to 591 and 3, to get
591 = 3 x 197 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 591 is 3
Notice that 3 = HCF(591,3) .
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Frequently Asked Questions on HCF of 687, 945, 591 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 687, 945, 591?
Answer: HCF of 687, 945, 591 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 945, 591 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 945, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.