Highest Common Factor of 522, 3502 using Euclid's algorithm
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, 3502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 3502 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, 3502 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, 3502 is 2.
HCF(522, 3502) = 2
HCF of 522, 3502 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 522, 3502 is 2.
Highest Common Factor of 522,3502 is 2
Step 1: Since 3502 > 522, we apply the division lemma to 3502 and 522, to get
3502 = 522 x 6 + 370
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 370 and 522, to get
522 = 370 x 1 + 152
Step 3: We consider the new divisor 370 and the new remainder 152, and apply the division lemma to get
370 = 152 x 2 + 66
We consider the new divisor 152 and the new remainder 66,and apply the division lemma to get
152 = 66 x 2 + 20
We consider the new divisor 66 and the new remainder 20,and apply the division lemma to get
66 = 20 x 3 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 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 522 and 3502 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(66,20) = HCF(152,66) = HCF(370,152) = HCF(522,370) = HCF(3502,522) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 522, 3502 using Euclid's Algorithm
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, 3502?
Answer: HCF of 522, 3502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 3502 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 3502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.