Highest Common Factor of 920, 416, 522 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 920, 416, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 920, 416, 522 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 920, 416, 522 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 920, 416, 522 is 2.
HCF(920, 416, 522) = 2
HCF of 920, 416, 522 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 920, 416, 522 is 2.
Highest Common Factor of 920,416,522 is 2
Step 1: Since 920 > 416, we apply the division lemma to 920 and 416, to get
920 = 416 x 2 + 88
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 88 and 416, to get
416 = 88 x 4 + 64
Step 3: We consider the new divisor 88 and the new remainder 64, and apply the division lemma to get
88 = 64 x 1 + 24
We consider the new divisor 64 and the new remainder 24,and apply the division lemma to get
64 = 24 x 2 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 920 and 416 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(88,64) = HCF(416,88) = HCF(920,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 522 > 8, we apply the division lemma to 522 and 8, to get
522 = 8 x 65 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 522 is 2
Notice that 2 = HCF(8,2) = HCF(522,8) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 920, 416, 522 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 920, 416, 522?
Answer: HCF of 920, 416, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 920, 416, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 920, 416, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.