Highest Common Factor of 67, 987, 722 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 67, 987, 722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 67, 987, 722 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 67, 987, 722 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 67, 987, 722 is 1.
HCF(67, 987, 722) = 1
HCF of 67, 987, 722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 67, 987, 722 is 1.
Highest Common Factor of 67,987,722 is 1
Step 1: Since 987 > 67, we apply the division lemma to 987 and 67, to get
987 = 67 x 14 + 49
Step 2: Since the reminder 67 ≠ 0, we apply division lemma to 49 and 67, to get
67 = 49 x 1 + 18
Step 3: We consider the new divisor 49 and the new remainder 18, and apply the division lemma to get
49 = 18 x 2 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 67 and 987 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(49,18) = HCF(67,49) = HCF(987,67) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 722 > 1, we apply the division lemma to 722 and 1, to get
722 = 1 x 722 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 722 is 1
Notice that 1 = HCF(722,1) .
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Frequently Asked Questions on HCF of 67, 987, 722 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 67, 987, 722?
Answer: HCF of 67, 987, 722 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 67, 987, 722 using Euclid's Algorithm?
Answer: For arbitrary numbers 67, 987, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.