Highest Common Factor of 987, 717 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 987, 717 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 717 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 987, 717 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 987, 717 is 3.
HCF(987, 717) = 3
HCF of 987, 717 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 717 is 3.
Highest Common Factor of 987,717 is 3
Step 1: Since 987 > 717, we apply the division lemma to 987 and 717, to get
987 = 717 x 1 + 270
Step 2: Since the reminder 717 ≠ 0, we apply division lemma to 270 and 717, to get
717 = 270 x 2 + 177
Step 3: We consider the new divisor 270 and the new remainder 177, and apply the division lemma to get
270 = 177 x 1 + 93
We consider the new divisor 177 and the new remainder 93,and apply the division lemma to get
177 = 93 x 1 + 84
We consider the new divisor 93 and the new remainder 84,and apply the division lemma to get
93 = 84 x 1 + 9
We consider the new divisor 84 and the new remainder 9,and apply the division lemma to get
84 = 9 x 9 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 987 and 717 is 3
Notice that 3 = HCF(9,3) = HCF(84,9) = HCF(93,84) = HCF(177,93) = HCF(270,177) = HCF(717,270) = HCF(987,717) .
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Frequently Asked Questions on HCF of 987, 717 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 987, 717?
Answer: HCF of 987, 717 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 717 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 717 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.