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 522, 8302, 8432 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 8302, 8432 is 2 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 522, 8302, 8432 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 522, 8302, 8432 is 2.
HCF(522, 8302, 8432) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 522, 8302, 8432 is 2.
Step 1: Since 8302 > 522, we apply the division lemma to 8302 and 522, to get
8302 = 522 x 15 + 472
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 472 and 522, to get
522 = 472 x 1 + 50
Step 3: We consider the new divisor 472 and the new remainder 50, and apply the division lemma to get
472 = 50 x 9 + 22
We consider the new divisor 50 and the new remainder 22,and apply the division lemma to get
50 = 22 x 2 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 522 and 8302 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(472,50) = HCF(522,472) = HCF(8302,522) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8432 > 2, we apply the division lemma to 8432 and 2, to get
8432 = 2 x 4216 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8432 is 2
Notice that 2 = HCF(8432,2) .
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 522, 8302, 8432?
Answer: HCF of 522, 8302, 8432 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 8302, 8432 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 8302, 8432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.