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 523, 921, 270, 98 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 523, 921, 270, 98 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 523, 921, 270, 98 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 523, 921, 270, 98 is 1.
HCF(523, 921, 270, 98) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 523, 921, 270, 98 is 1.
Step 1: Since 921 > 523, we apply the division lemma to 921 and 523, to get
921 = 523 x 1 + 398
Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 398 and 523, to get
523 = 398 x 1 + 125
Step 3: We consider the new divisor 398 and the new remainder 125, and apply the division lemma to get
398 = 125 x 3 + 23
We consider the new divisor 125 and the new remainder 23,and apply the division lemma to get
125 = 23 x 5 + 10
We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get
23 = 10 x 2 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 921 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(125,23) = HCF(398,125) = HCF(523,398) = HCF(921,523) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 1, we apply the division lemma to 270 and 1, to get
270 = 1 x 270 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 270 is 1
Notice that 1 = HCF(270,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 98 > 1, we apply the division lemma to 98 and 1, to get
98 = 1 x 98 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 98 is 1
Notice that 1 = HCF(98,1) .
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 523, 921, 270, 98?
Answer: HCF of 523, 921, 270, 98 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 523, 921, 270, 98 using Euclid's Algorithm?
Answer: For arbitrary numbers 523, 921, 270, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.