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 663, 967, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 967, 851 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 663, 967, 851 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 663, 967, 851 is 1.
HCF(663, 967, 851) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 967, 851 is 1.
Step 1: Since 967 > 663, we apply the division lemma to 967 and 663, to get
967 = 663 x 1 + 304
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 304 and 663, to get
663 = 304 x 2 + 55
Step 3: We consider the new divisor 304 and the new remainder 55, and apply the division lemma to get
304 = 55 x 5 + 29
We consider the new divisor 55 and the new remainder 29,and apply the division lemma to get
55 = 29 x 1 + 26
We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get
29 = 26 x 1 + 3
We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get
26 = 3 x 8 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 663 and 967 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(55,29) = HCF(304,55) = HCF(663,304) = HCF(967,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 851 > 1, we apply the division lemma to 851 and 1, to get
851 = 1 x 851 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 851 is 1
Notice that 1 = HCF(851,1) .
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 663, 967, 851?
Answer: HCF of 663, 967, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 967, 851 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 967, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.