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 564, 870, 815, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 870, 815, 991 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 564, 870, 815, 991 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 564, 870, 815, 991 is 1.
HCF(564, 870, 815, 991) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 870, 815, 991 is 1.
Step 1: Since 870 > 564, we apply the division lemma to 870 and 564, to get
870 = 564 x 1 + 306
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 306 and 564, to get
564 = 306 x 1 + 258
Step 3: We consider the new divisor 306 and the new remainder 258, and apply the division lemma to get
306 = 258 x 1 + 48
We consider the new divisor 258 and the new remainder 48,and apply the division lemma to get
258 = 48 x 5 + 18
We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get
48 = 18 x 2 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 564 and 870 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(258,48) = HCF(306,258) = HCF(564,306) = HCF(870,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 815 > 6, we apply the division lemma to 815 and 6, to get
815 = 6 x 135 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 815 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(815,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 991 > 1, we apply the division lemma to 991 and 1, to get
991 = 1 x 991 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 991 is 1
Notice that 1 = HCF(991,1) .
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 564, 870, 815, 991?
Answer: HCF of 564, 870, 815, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 870, 815, 991 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 870, 815, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.