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 799, 972, 208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 799, 972, 208 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 799, 972, 208 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 799, 972, 208 is 1.
HCF(799, 972, 208) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 799, 972, 208 is 1.
Step 1: Since 972 > 799, we apply the division lemma to 972 and 799, to get
972 = 799 x 1 + 173
Step 2: Since the reminder 799 ≠ 0, we apply division lemma to 173 and 799, to get
799 = 173 x 4 + 107
Step 3: We consider the new divisor 173 and the new remainder 107, and apply the division lemma to get
173 = 107 x 1 + 66
We consider the new divisor 107 and the new remainder 66,and apply the division lemma to get
107 = 66 x 1 + 41
We consider the new divisor 66 and the new remainder 41,and apply the division lemma to get
66 = 41 x 1 + 25
We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get
41 = 25 x 1 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 799 and 972 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(66,41) = HCF(107,66) = HCF(173,107) = HCF(799,173) = HCF(972,799) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 208 > 1, we apply the division lemma to 208 and 1, to get
208 = 1 x 208 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 208 is 1
Notice that 1 = HCF(208,1) .
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 799, 972, 208?
Answer: HCF of 799, 972, 208 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 799, 972, 208 using Euclid's Algorithm?
Answer: For arbitrary numbers 799, 972, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.