Highest Common Factor of 672, 548, 199 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 672, 548, 199 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 548, 199 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 672, 548, 199 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 672, 548, 199 is 1.
HCF(672, 548, 199) = 1
HCF of 672, 548, 199 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 548, 199 is 1.
Highest Common Factor of 672,548,199 is 1
Step 1: Since 672 > 548, we apply the division lemma to 672 and 548, to get
672 = 548 x 1 + 124
Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 124 and 548, to get
548 = 124 x 4 + 52
Step 3: We consider the new divisor 124 and the new remainder 52, and apply the division lemma to get
124 = 52 x 2 + 20
We consider the new divisor 52 and the new remainder 20,and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 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 672 and 548 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(124,52) = HCF(548,124) = HCF(672,548) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 199 > 4, we apply the division lemma to 199 and 4, to get
199 = 4 x 49 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 199 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(199,4) .
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Frequently Asked Questions on HCF of 672, 548, 199 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 672, 548, 199?
Answer: HCF of 672, 548, 199 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 548, 199 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 548, 199 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
