Highest Common Factor of 272, 987, 77 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 272, 987, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 987, 77 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 272, 987, 77 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 272, 987, 77 is 1.
HCF(272, 987, 77) = 1
HCF of 272, 987, 77 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 272, 987, 77 is 1.
Highest Common Factor of 272,987,77 is 1
Step 1: Since 987 > 272, we apply the division lemma to 987 and 272, to get
987 = 272 x 3 + 171
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 171 and 272, to get
272 = 171 x 1 + 101
Step 3: We consider the new divisor 171 and the new remainder 101, and apply the division lemma to get
171 = 101 x 1 + 70
We consider the new divisor 101 and the new remainder 70,and apply the division lemma to get
101 = 70 x 1 + 31
We consider the new divisor 70 and the new remainder 31,and apply the division lemma to get
70 = 31 x 2 + 8
We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get
31 = 8 x 3 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 272 and 987 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(70,31) = HCF(101,70) = HCF(171,101) = HCF(272,171) = HCF(987,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get
77 = 1 x 77 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1
Notice that 1 = HCF(77,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 272, 987, 77 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 272, 987, 77?
Answer: HCF of 272, 987, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 987, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 987, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
