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 81, 55, 88, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 81, 55, 88, 106 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 81, 55, 88, 106 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 81, 55, 88, 106 is 1.
HCF(81, 55, 88, 106) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 81, 55, 88, 106 is 1.
Step 1: Since 81 > 55, we apply the division lemma to 81 and 55, to get
81 = 55 x 1 + 26
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 26 and 55, to get
55 = 26 x 2 + 3
Step 3: We consider the new divisor 26 and the new remainder 3, and apply the division lemma to get
26 = 3 x 8 + 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 81 and 55 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(55,26) = HCF(81,55) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 88 > 1, we apply the division lemma to 88 and 1, to get
88 = 1 x 88 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 88 is 1
Notice that 1 = HCF(88,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 1, we apply the division lemma to 106 and 1, to get
106 = 1 x 106 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 106 is 1
Notice that 1 = HCF(106,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 81, 55, 88, 106?
Answer: HCF of 81, 55, 88, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 81, 55, 88, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 81, 55, 88, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.