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 644, 371, 776 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 644, 371, 776 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 644, 371, 776 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 644, 371, 776 is 1.
HCF(644, 371, 776) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 644, 371, 776 is 1.
Step 1: Since 644 > 371, we apply the division lemma to 644 and 371, to get
644 = 371 x 1 + 273
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 273 and 371, to get
371 = 273 x 1 + 98
Step 3: We consider the new divisor 273 and the new remainder 98, and apply the division lemma to get
273 = 98 x 2 + 77
We consider the new divisor 98 and the new remainder 77,and apply the division lemma to get
98 = 77 x 1 + 21
We consider the new divisor 77 and the new remainder 21,and apply the division lemma to get
77 = 21 x 3 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 644 and 371 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(77,21) = HCF(98,77) = HCF(273,98) = HCF(371,273) = HCF(644,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 776 > 7, we apply the division lemma to 776 and 7, to get
776 = 7 x 110 + 6
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 6 and 7, to get
7 = 6 x 1 + 1
Step 3: We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 776 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(776,7) .
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 644, 371, 776?
Answer: HCF of 644, 371, 776 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 644, 371, 776 using Euclid's Algorithm?
Answer: For arbitrary numbers 644, 371, 776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.