Highest Common Factor of 10, 16, 89, 22 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 10, 16, 89, 22 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 10, 16, 89, 22 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 10, 16, 89, 22 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 10, 16, 89, 22 is 1.
HCF(10, 16, 89, 22) = 1
HCF of 10, 16, 89, 22 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 10, 16, 89, 22 is 1.
Highest Common Factor of 10,16,89,22 is 1
Step 1: Since 16 > 10, we apply the division lemma to 16 and 10, to get
16 = 10 x 1 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: 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 10 and 16 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 89 > 2, we apply the division lemma to 89 and 2, to get
89 = 2 x 44 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 89 is 1
Notice that 1 = HCF(2,1) = HCF(89,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22 > 1, we apply the division lemma to 22 and 1, to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22 is 1
Notice that 1 = HCF(22,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 10, 16, 89, 22 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 10, 16, 89, 22?
Answer: HCF of 10, 16, 89, 22 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 10, 16, 89, 22 using Euclid's Algorithm?
Answer: For arbitrary numbers 10, 16, 89, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.