Highest Common Factor of 912, 7098, 7430 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 912, 7098, 7430 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 7098, 7430 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 912, 7098, 7430 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 912, 7098, 7430 is 2.
HCF(912, 7098, 7430) = 2
HCF of 912, 7098, 7430 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 7098, 7430 is 2.
Highest Common Factor of 912,7098,7430 is 2
Step 1: Since 7098 > 912, we apply the division lemma to 7098 and 912, to get
7098 = 912 x 7 + 714
Step 2: Since the reminder 912 ≠ 0, we apply division lemma to 714 and 912, to get
912 = 714 x 1 + 198
Step 3: We consider the new divisor 714 and the new remainder 198, and apply the division lemma to get
714 = 198 x 3 + 120
We consider the new divisor 198 and the new remainder 120,and apply the division lemma to get
198 = 120 x 1 + 78
We consider the new divisor 120 and the new remainder 78,and apply the division lemma to get
120 = 78 x 1 + 42
We consider the new divisor 78 and the new remainder 42,and apply the division lemma to get
78 = 42 x 1 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 912 and 7098 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(78,42) = HCF(120,78) = HCF(198,120) = HCF(714,198) = HCF(912,714) = HCF(7098,912) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7430 > 6, we apply the division lemma to 7430 and 6, to get
7430 = 6 x 1238 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 7430 is 2
Notice that 2 = HCF(6,2) = HCF(7430,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 912, 7098, 7430 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 912, 7098, 7430?
Answer: HCF of 912, 7098, 7430 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 7098, 7430 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 7098, 7430 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.