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 4222, 1434, 34413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4222, 1434, 34413 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 4222, 1434, 34413 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 4222, 1434, 34413 is 1.
HCF(4222, 1434, 34413) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4222, 1434, 34413 is 1.
Step 1: Since 4222 > 1434, we apply the division lemma to 4222 and 1434, to get
4222 = 1434 x 2 + 1354
Step 2: Since the reminder 1434 ≠ 0, we apply division lemma to 1354 and 1434, to get
1434 = 1354 x 1 + 80
Step 3: We consider the new divisor 1354 and the new remainder 80, and apply the division lemma to get
1354 = 80 x 16 + 74
We consider the new divisor 80 and the new remainder 74,and apply the division lemma to get
80 = 74 x 1 + 6
We consider the new divisor 74 and the new remainder 6,and apply the division lemma to get
74 = 6 x 12 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4222 and 1434 is 2
Notice that 2 = HCF(6,2) = HCF(74,6) = HCF(80,74) = HCF(1354,80) = HCF(1434,1354) = HCF(4222,1434) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34413 > 2, we apply the division lemma to 34413 and 2, to get
34413 = 2 x 17206 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 34413 is 1
Notice that 1 = HCF(2,1) = HCF(34413,2) .
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 4222, 1434, 34413?
Answer: HCF of 4222, 1434, 34413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4222, 1434, 34413 using Euclid's Algorithm?
Answer: For arbitrary numbers 4222, 1434, 34413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.