Highest Common Factor of 38, 144, 222 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 38, 144, 222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 38, 144, 222 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 38, 144, 222 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 38, 144, 222 is 2.
HCF(38, 144, 222) = 2
HCF of 38, 144, 222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 38, 144, 222 is 2.
Highest Common Factor of 38,144,222 is 2
Step 1: Since 144 > 38, we apply the division lemma to 144 and 38, to get
144 = 38 x 3 + 30
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 30 and 38, to get
38 = 30 x 1 + 8
Step 3: We consider the new divisor 30 and the new remainder 8, and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 38 and 144 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(144,38) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 222 > 2, we apply the division lemma to 222 and 2, to get
222 = 2 x 111 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 222 is 2
Notice that 2 = HCF(222,2) .
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Frequently Asked Questions on HCF of 38, 144, 222 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 38, 144, 222?
Answer: HCF of 38, 144, 222 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 38, 144, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 38, 144, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.