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 8184, 4961, 69759 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8184, 4961, 69759 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 8184, 4961, 69759 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 8184, 4961, 69759 is 1.
HCF(8184, 4961, 69759) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8184, 4961, 69759 is 1.
Step 1: Since 8184 > 4961, we apply the division lemma to 8184 and 4961, to get
8184 = 4961 x 1 + 3223
Step 2: Since the reminder 4961 ≠ 0, we apply division lemma to 3223 and 4961, to get
4961 = 3223 x 1 + 1738
Step 3: We consider the new divisor 3223 and the new remainder 1738, and apply the division lemma to get
3223 = 1738 x 1 + 1485
We consider the new divisor 1738 and the new remainder 1485,and apply the division lemma to get
1738 = 1485 x 1 + 253
We consider the new divisor 1485 and the new remainder 253,and apply the division lemma to get
1485 = 253 x 5 + 220
We consider the new divisor 253 and the new remainder 220,and apply the division lemma to get
253 = 220 x 1 + 33
We consider the new divisor 220 and the new remainder 33,and apply the division lemma to get
220 = 33 x 6 + 22
We consider the new divisor 33 and the new remainder 22,and apply the division lemma to get
33 = 22 x 1 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 8184 and 4961 is 11
Notice that 11 = HCF(22,11) = HCF(33,22) = HCF(220,33) = HCF(253,220) = HCF(1485,253) = HCF(1738,1485) = HCF(3223,1738) = HCF(4961,3223) = HCF(8184,4961) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69759 > 11, we apply the division lemma to 69759 and 11, to get
69759 = 11 x 6341 + 8
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get
11 = 8 x 1 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 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 11 and 69759 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(69759,11) .
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 8184, 4961, 69759?
Answer: HCF of 8184, 4961, 69759 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8184, 4961, 69759 using Euclid's Algorithm?
Answer: For arbitrary numbers 8184, 4961, 69759 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.