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 1698, 7656 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1698, 7656 is 6 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 1698, 7656 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 1698, 7656 is 6.
HCF(1698, 7656) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1698, 7656 is 6.
Step 1: Since 7656 > 1698, we apply the division lemma to 7656 and 1698, to get
7656 = 1698 x 4 + 864
Step 2: Since the reminder 1698 ≠ 0, we apply division lemma to 864 and 1698, to get
1698 = 864 x 1 + 834
Step 3: We consider the new divisor 864 and the new remainder 834, and apply the division lemma to get
864 = 834 x 1 + 30
We consider the new divisor 834 and the new remainder 30,and apply the division lemma to get
834 = 30 x 27 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1698 and 7656 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(834,30) = HCF(864,834) = HCF(1698,864) = HCF(7656,1698) .
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 1698, 7656?
Answer: HCF of 1698, 7656 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1698, 7656 using Euclid's Algorithm?
Answer: For arbitrary numbers 1698, 7656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.