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 319, 870, 866 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 319, 870, 866 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 319, 870, 866 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 319, 870, 866 is 1.
HCF(319, 870, 866) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 319, 870, 866 is 1.
Step 1: Since 870 > 319, we apply the division lemma to 870 and 319, to get
870 = 319 x 2 + 232
Step 2: Since the reminder 319 ≠ 0, we apply division lemma to 232 and 319, to get
319 = 232 x 1 + 87
Step 3: We consider the new divisor 232 and the new remainder 87, and apply the division lemma to get
232 = 87 x 2 + 58
We consider the new divisor 87 and the new remainder 58,and apply the division lemma to get
87 = 58 x 1 + 29
We consider the new divisor 58 and the new remainder 29,and apply the division lemma to get
58 = 29 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 319 and 870 is 29
Notice that 29 = HCF(58,29) = HCF(87,58) = HCF(232,87) = HCF(319,232) = HCF(870,319) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 866 > 29, we apply the division lemma to 866 and 29, to get
866 = 29 x 29 + 25
Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 25 and 29, to get
29 = 25 x 1 + 4
Step 3: We consider the new divisor 25 and the new remainder 4, and apply the division lemma to get
25 = 4 x 6 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 866 is 1
Notice that 1 = HCF(4,1) = HCF(25,4) = HCF(29,25) = HCF(866,29) .
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 319, 870, 866?
Answer: HCF of 319, 870, 866 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 319, 870, 866 using Euclid's Algorithm?
Answer: For arbitrary numbers 319, 870, 866 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.