Highest Common Factor of 378, 238, 655 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 378, 238, 655 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 238, 655 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 378, 238, 655 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 378, 238, 655 is 1.
HCF(378, 238, 655) = 1
HCF of 378, 238, 655 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 238, 655 is 1.
Highest Common Factor of 378,238,655 is 1
Step 1: Since 378 > 238, we apply the division lemma to 378 and 238, to get
378 = 238 x 1 + 140
Step 2: Since the reminder 238 ≠ 0, we apply division lemma to 140 and 238, to get
238 = 140 x 1 + 98
Step 3: We consider the new divisor 140 and the new remainder 98, and apply the division lemma to get
140 = 98 x 1 + 42
We consider the new divisor 98 and the new remainder 42,and apply the division lemma to get
98 = 42 x 2 + 14
We consider the new divisor 42 and the new remainder 14,and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 378 and 238 is 14
Notice that 14 = HCF(42,14) = HCF(98,42) = HCF(140,98) = HCF(238,140) = HCF(378,238) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 655 > 14, we apply the division lemma to 655 and 14, to get
655 = 14 x 46 + 11
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 11 and 14, to get
14 = 11 x 1 + 3
Step 3: We consider the new divisor 11 and the new remainder 3, and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 14 and 655 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(655,14) .
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Frequently Asked Questions on HCF of 378, 238, 655 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 378, 238, 655?
Answer: HCF of 378, 238, 655 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 238, 655 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 238, 655 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
