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, 920, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 920, 133 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 522, 920, 133 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, 920, 133 is 1.
HCF(522, 920, 133) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 522, 920, 133 is 1.
Step 1: Since 920 > 522, we apply the division lemma to 920 and 522, to get
920 = 522 x 1 + 398
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 398 and 522, to get
522 = 398 x 1 + 124
Step 3: We consider the new divisor 398 and the new remainder 124, and apply the division lemma to get
398 = 124 x 3 + 26
We consider the new divisor 124 and the new remainder 26,and apply the division lemma to get
124 = 26 x 4 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 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 920 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(124,26) = HCF(398,124) = HCF(522,398) = HCF(920,522) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 133 > 2, we apply the division lemma to 133 and 2, to get
133 = 2 x 66 + 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 133 is 1
Notice that 1 = HCF(2,1) = HCF(133,2) .
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, 920, 133?
Answer: HCF of 522, 920, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 920, 133 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 920, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.