Highest Common Factor of 987, 692, 684 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, 692, 684 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 692, 684 is 1 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, 692, 684 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, 692, 684 is 1.
HCF(987, 692, 684) = 1
HCF of 987, 692, 684 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, 692, 684 is 1.
Highest Common Factor of 987,692,684 is 1
Step 1: Since 987 > 692, we apply the division lemma to 987 and 692, to get
987 = 692 x 1 + 295
Step 2: Since the reminder 692 ≠ 0, we apply division lemma to 295 and 692, to get
692 = 295 x 2 + 102
Step 3: We consider the new divisor 295 and the new remainder 102, and apply the division lemma to get
295 = 102 x 2 + 91
We consider the new divisor 102 and the new remainder 91,and apply the division lemma to get
102 = 91 x 1 + 11
We consider the new divisor 91 and the new remainder 11,and apply the division lemma to get
91 = 11 x 8 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 987 and 692 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(91,11) = HCF(102,91) = HCF(295,102) = HCF(692,295) = HCF(987,692) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 684 > 1, we apply the division lemma to 684 and 1, to get
684 = 1 x 684 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 684 is 1
Notice that 1 = HCF(684,1) .
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Frequently Asked Questions on HCF of 987, 692, 684 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, 692, 684?
Answer: HCF of 987, 692, 684 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 692, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 692, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.