Highest Common Factor of 555, 378, 118 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 555, 378, 118 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 555, 378, 118 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 555, 378, 118 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 555, 378, 118 is 1.
HCF(555, 378, 118) = 1
HCF of 555, 378, 118 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 555, 378, 118 is 1.
Highest Common Factor of 555,378,118 is 1
Step 1: Since 555 > 378, we apply the division lemma to 555 and 378, to get
555 = 378 x 1 + 177
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 177 and 378, to get
378 = 177 x 2 + 24
Step 3: We consider the new divisor 177 and the new remainder 24, and apply the division lemma to get
177 = 24 x 7 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 555 and 378 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(177,24) = HCF(378,177) = HCF(555,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 3, we apply the division lemma to 118 and 3, to get
118 = 3 x 39 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 118 is 1
Notice that 1 = HCF(3,1) = HCF(118,3) .
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Frequently Asked Questions on HCF of 555, 378, 118 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 555, 378, 118?
Answer: HCF of 555, 378, 118 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 555, 378, 118 using Euclid's Algorithm?
Answer: For arbitrary numbers 555, 378, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.