Highest Common Factor of 548, 666, 113 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 548, 666, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 666, 113 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 548, 666, 113 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 548, 666, 113 is 1.
HCF(548, 666, 113) = 1
HCF of 548, 666, 113 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 548, 666, 113 is 1.
Highest Common Factor of 548,666,113 is 1
Step 1: Since 666 > 548, we apply the division lemma to 666 and 548, to get
666 = 548 x 1 + 118
Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 118 and 548, to get
548 = 118 x 4 + 76
Step 3: We consider the new divisor 118 and the new remainder 76, and apply the division lemma to get
118 = 76 x 1 + 42
We consider the new divisor 76 and the new remainder 42,and apply the division lemma to get
76 = 42 x 1 + 34
We consider the new divisor 42 and the new remainder 34,and apply the division lemma to get
42 = 34 x 1 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 548 and 666 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(42,34) = HCF(76,42) = HCF(118,76) = HCF(548,118) = HCF(666,548) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 2, we apply the division lemma to 113 and 2, to get
113 = 2 x 56 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 113 is 1
Notice that 1 = HCF(2,1) = HCF(113,2) .
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Frequently Asked Questions on HCF of 548, 666, 113 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 548, 666, 113?
Answer: HCF of 548, 666, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 666, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 666, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.