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 4219, 1635, 22998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4219, 1635, 22998 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 4219, 1635, 22998 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 4219, 1635, 22998 is 1.
HCF(4219, 1635, 22998) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4219, 1635, 22998 is 1.
Step 1: Since 4219 > 1635, we apply the division lemma to 4219 and 1635, to get
4219 = 1635 x 2 + 949
Step 2: Since the reminder 1635 ≠ 0, we apply division lemma to 949 and 1635, to get
1635 = 949 x 1 + 686
Step 3: We consider the new divisor 949 and the new remainder 686, and apply the division lemma to get
949 = 686 x 1 + 263
We consider the new divisor 686 and the new remainder 263,and apply the division lemma to get
686 = 263 x 2 + 160
We consider the new divisor 263 and the new remainder 160,and apply the division lemma to get
263 = 160 x 1 + 103
We consider the new divisor 160 and the new remainder 103,and apply the division lemma to get
160 = 103 x 1 + 57
We consider the new divisor 103 and the new remainder 57,and apply the division lemma to get
103 = 57 x 1 + 46
We consider the new divisor 57 and the new remainder 46,and apply the division lemma to get
57 = 46 x 1 + 11
We consider the new divisor 46 and the new remainder 11,and apply the division lemma to get
46 = 11 x 4 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 4219 and 1635 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(46,11) = HCF(57,46) = HCF(103,57) = HCF(160,103) = HCF(263,160) = HCF(686,263) = HCF(949,686) = HCF(1635,949) = HCF(4219,1635) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 22998 > 1, we apply the division lemma to 22998 and 1, to get
22998 = 1 x 22998 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22998 is 1
Notice that 1 = HCF(22998,1) .
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 4219, 1635, 22998?
Answer: HCF of 4219, 1635, 22998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4219, 1635, 22998 using Euclid's Algorithm?
Answer: For arbitrary numbers 4219, 1635, 22998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.