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 467, 768, 401, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 467, 768, 401, 51 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 467, 768, 401, 51 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 467, 768, 401, 51 is 1.
HCF(467, 768, 401, 51) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 467, 768, 401, 51 is 1.
Step 1: Since 768 > 467, we apply the division lemma to 768 and 467, to get
768 = 467 x 1 + 301
Step 2: Since the reminder 467 ≠ 0, we apply division lemma to 301 and 467, to get
467 = 301 x 1 + 166
Step 3: We consider the new divisor 301 and the new remainder 166, and apply the division lemma to get
301 = 166 x 1 + 135
We consider the new divisor 166 and the new remainder 135,and apply the division lemma to get
166 = 135 x 1 + 31
We consider the new divisor 135 and the new remainder 31,and apply the division lemma to get
135 = 31 x 4 + 11
We consider the new divisor 31 and the new remainder 11,and apply the division lemma to get
31 = 11 x 2 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
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 467 and 768 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(31,11) = HCF(135,31) = HCF(166,135) = HCF(301,166) = HCF(467,301) = HCF(768,467) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 401 > 1, we apply the division lemma to 401 and 1, to get
401 = 1 x 401 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 401 is 1
Notice that 1 = HCF(401,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 1, we apply the division lemma to 51 and 1, to get
51 = 1 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51 is 1
Notice that 1 = HCF(51,1) .
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 467, 768, 401, 51?
Answer: HCF of 467, 768, 401, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 467, 768, 401, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 467, 768, 401, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.