Highest Common Factor of 672, 768, 274, 68 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, 768, 274, 68 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 768, 274, 68 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 672, 768, 274, 68 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, 768, 274, 68 is 2.
HCF(672, 768, 274, 68) = 2
HCF of 672, 768, 274, 68 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, 768, 274, 68 is 2.
Highest Common Factor of 672,768,274,68 is 2
Step 1: Since 768 > 672, we apply the division lemma to 768 and 672, to get
768 = 672 x 1 + 96
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 96 and 672, to get
672 = 96 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 96, the HCF of 672 and 768 is 96
Notice that 96 = HCF(672,96) = HCF(768,672) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 96, we apply the division lemma to 274 and 96, to get
274 = 96 x 2 + 82
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 82 and 96, to get
96 = 82 x 1 + 14
Step 3: We consider the new divisor 82 and the new remainder 14, and apply the division lemma to get
82 = 14 x 5 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 96 and 274 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(82,14) = HCF(96,82) = HCF(274,96) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 2, we apply the division lemma to 68 and 2, to get
68 = 2 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 68 is 2
Notice that 2 = HCF(68,2) .
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Frequently Asked Questions on HCF of 672, 768, 274, 68 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, 768, 274, 68?
Answer: HCF of 672, 768, 274, 68 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 768, 274, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 768, 274, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.