Highest Common Factor of 698, 8924 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 698, 8924 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 698, 8924 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 698, 8924 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 698, 8924 is 2.
HCF(698, 8924) = 2
HCF of 698, 8924 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 698, 8924 is 2.
Highest Common Factor of 698,8924 is 2
Step 1: Since 8924 > 698, we apply the division lemma to 8924 and 698, to get
8924 = 698 x 12 + 548
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 548 and 698, to get
698 = 548 x 1 + 150
Step 3: We consider the new divisor 548 and the new remainder 150, and apply the division lemma to get
548 = 150 x 3 + 98
We consider the new divisor 150 and the new remainder 98,and apply the division lemma to get
150 = 98 x 1 + 52
We consider the new divisor 98 and the new remainder 52,and apply the division lemma to get
98 = 52 x 1 + 46
We consider the new divisor 52 and the new remainder 46,and apply the division lemma to get
52 = 46 x 1 + 6
We consider the new divisor 46 and the new remainder 6,and apply the division lemma to get
46 = 6 x 7 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 8924 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(52,46) = HCF(98,52) = HCF(150,98) = HCF(548,150) = HCF(698,548) = HCF(8924,698) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 698, 8924 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 698, 8924?
Answer: HCF of 698, 8924 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 698, 8924 using Euclid's Algorithm?
Answer: For arbitrary numbers 698, 8924 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.