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 310, 810, 892, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 810, 892, 221 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 310, 810, 892, 221 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 310, 810, 892, 221 is 1.
HCF(310, 810, 892, 221) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 810, 892, 221 is 1.
Step 1: Since 810 > 310, we apply the division lemma to 810 and 310, to get
810 = 310 x 2 + 190
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 190 and 310, to get
310 = 190 x 1 + 120
Step 3: We consider the new divisor 190 and the new remainder 120, and apply the division lemma to get
190 = 120 x 1 + 70
We consider the new divisor 120 and the new remainder 70,and apply the division lemma to get
120 = 70 x 1 + 50
We consider the new divisor 70 and the new remainder 50,and apply the division lemma to get
70 = 50 x 1 + 20
We consider the new divisor 50 and the new remainder 20,and apply the division lemma to get
50 = 20 x 2 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 310 and 810 is 10
Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(70,50) = HCF(120,70) = HCF(190,120) = HCF(310,190) = HCF(810,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 892 > 10, we apply the division lemma to 892 and 10, to get
892 = 10 x 89 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 892 is 2
Notice that 2 = HCF(10,2) = HCF(892,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 221 > 2, we apply the division lemma to 221 and 2, to get
221 = 2 x 110 + 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 221 is 1
Notice that 1 = HCF(2,1) = HCF(221,2) .
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 310, 810, 892, 221?
Answer: HCF of 310, 810, 892, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 810, 892, 221 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 810, 892, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.