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 768, 657, 721, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 657, 721, 338 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 768, 657, 721, 338 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 768, 657, 721, 338 is 1.
HCF(768, 657, 721, 338) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 657, 721, 338 is 1.
Step 1: Since 768 > 657, we apply the division lemma to 768 and 657, to get
768 = 657 x 1 + 111
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 111 and 657, to get
657 = 111 x 5 + 102
Step 3: We consider the new divisor 111 and the new remainder 102, and apply the division lemma to get
111 = 102 x 1 + 9
We consider the new divisor 102 and the new remainder 9,and apply the division lemma to get
102 = 9 x 11 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 768 and 657 is 3
Notice that 3 = HCF(9,3) = HCF(102,9) = HCF(111,102) = HCF(657,111) = HCF(768,657) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 721 > 3, we apply the division lemma to 721 and 3, to get
721 = 3 x 240 + 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 721 is 1
Notice that 1 = HCF(3,1) = HCF(721,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 1, we apply the division lemma to 338 and 1, to get
338 = 1 x 338 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 338 is 1
Notice that 1 = HCF(338,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 768, 657, 721, 338?
Answer: HCF of 768, 657, 721, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 657, 721, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 657, 721, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.