Highest Common Factor of 236, 372, 254 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 236, 372, 254 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 236, 372, 254 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 236, 372, 254 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 236, 372, 254 is 2.
HCF(236, 372, 254) = 2
HCF of 236, 372, 254 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 236, 372, 254 is 2.
Highest Common Factor of 236,372,254 is 2
Step 1: Since 372 > 236, we apply the division lemma to 372 and 236, to get
372 = 236 x 1 + 136
Step 2: Since the reminder 236 ≠ 0, we apply division lemma to 136 and 236, to get
236 = 136 x 1 + 100
Step 3: We consider the new divisor 136 and the new remainder 100, and apply the division lemma to get
136 = 100 x 1 + 36
We consider the new divisor 100 and the new remainder 36,and apply the division lemma to get
100 = 36 x 2 + 28
We consider the new divisor 36 and the new remainder 28,and apply the division lemma to get
36 = 28 x 1 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 236 and 372 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(36,28) = HCF(100,36) = HCF(136,100) = HCF(236,136) = HCF(372,236) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 254 > 4, we apply the division lemma to 254 and 4, to get
254 = 4 x 63 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 254 is 2
Notice that 2 = HCF(4,2) = HCF(254,4) .
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Frequently Asked Questions on HCF of 236, 372, 254 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 236, 372, 254?
Answer: HCF of 236, 372, 254 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 236, 372, 254 using Euclid's Algorithm?
Answer: For arbitrary numbers 236, 372, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.