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 795, 657, 101, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 795, 657, 101, 21 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 795, 657, 101, 21 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 795, 657, 101, 21 is 1.
HCF(795, 657, 101, 21) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 795, 657, 101, 21 is 1.
Step 1: Since 795 > 657, we apply the division lemma to 795 and 657, to get
795 = 657 x 1 + 138
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 138 and 657, to get
657 = 138 x 4 + 105
Step 3: We consider the new divisor 138 and the new remainder 105, and apply the division lemma to get
138 = 105 x 1 + 33
We consider the new divisor 105 and the new remainder 33,and apply the division lemma to get
105 = 33 x 3 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 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 795 and 657 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(105,33) = HCF(138,105) = HCF(657,138) = HCF(795,657) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 101 > 3, we apply the division lemma to 101 and 3, to get
101 = 3 x 33 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 101 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(101,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
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 795, 657, 101, 21?
Answer: HCF of 795, 657, 101, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 795, 657, 101, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 795, 657, 101, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.