Highest Common Factor of 234, 298, 242, 16 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 234, 298, 242, 16 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 234, 298, 242, 16 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 234, 298, 242, 16 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 234, 298, 242, 16 is 2.
HCF(234, 298, 242, 16) = 2
HCF of 234, 298, 242, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 234, 298, 242, 16 is 2.
Highest Common Factor of 234,298,242,16 is 2
Step 1: Since 298 > 234, we apply the division lemma to 298 and 234, to get
298 = 234 x 1 + 64
Step 2: Since the reminder 234 ≠ 0, we apply division lemma to 64 and 234, to get
234 = 64 x 3 + 42
Step 3: We consider the new divisor 64 and the new remainder 42, and apply the division lemma to get
64 = 42 x 1 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 234 and 298 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(64,42) = HCF(234,64) = HCF(298,234) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 242 > 2, we apply the division lemma to 242 and 2, to get
242 = 2 x 121 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 242 is 2
Notice that 2 = HCF(242,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2
Notice that 2 = HCF(16,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 234, 298, 242, 16 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 234, 298, 242, 16?
Answer: HCF of 234, 298, 242, 16 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 234, 298, 242, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 234, 298, 242, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.