Highest Common Factor of 106, 90, 116, 220 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 106, 90, 116, 220 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 106, 90, 116, 220 is 2 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 106, 90, 116, 220 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 106, 90, 116, 220 is 2.
HCF(106, 90, 116, 220) = 2
HCF of 106, 90, 116, 220 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 106, 90, 116, 220 is 2.
Highest Common Factor of 106,90,116,220 is 2
Step 1: Since 106 > 90, we apply the division lemma to 106 and 90, to get
106 = 90 x 1 + 16
Step 2: Since the reminder 90 ≠ 0, we apply division lemma to 16 and 90, to get
90 = 16 x 5 + 10
Step 3: We consider the new divisor 16 and the new remainder 10, and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 106 and 90 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(90,16) = HCF(106,90) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 2, we apply the division lemma to 116 and 2, to get
116 = 2 x 58 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 116 is 2
Notice that 2 = HCF(116,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 220 > 2, we apply the division lemma to 220 and 2, to get
220 = 2 x 110 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 220 is 2
Notice that 2 = HCF(220,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 106, 90, 116, 220 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 106, 90, 116, 220?
Answer: HCF of 106, 90, 116, 220 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 106, 90, 116, 220 using Euclid's Algorithm?
Answer: For arbitrary numbers 106, 90, 116, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
