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 9688, 2116 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 9688, 2116 is 4 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 9688, 2116 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 9688, 2116 is 4.
HCF(9688, 2116) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9688, 2116 is 4.
Step 1: Since 9688 > 2116, we apply the division lemma to 9688 and 2116, to get
9688 = 2116 x 4 + 1224
Step 2: Since the reminder 2116 ≠ 0, we apply division lemma to 1224 and 2116, to get
2116 = 1224 x 1 + 892
Step 3: We consider the new divisor 1224 and the new remainder 892, and apply the division lemma to get
1224 = 892 x 1 + 332
We consider the new divisor 892 and the new remainder 332,and apply the division lemma to get
892 = 332 x 2 + 228
We consider the new divisor 332 and the new remainder 228,and apply the division lemma to get
332 = 228 x 1 + 104
We consider the new divisor 228 and the new remainder 104,and apply the division lemma to get
228 = 104 x 2 + 20
We consider the new divisor 104 and the new remainder 20,and apply the division lemma to get
104 = 20 x 5 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9688 and 2116 is 4
Notice that 4 = HCF(20,4) = HCF(104,20) = HCF(228,104) = HCF(332,228) = HCF(892,332) = HCF(1224,892) = HCF(2116,1224) = HCF(9688,2116) .
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 9688, 2116?
Answer: HCF of 9688, 2116 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9688, 2116 using Euclid's Algorithm?
Answer: For arbitrary numbers 9688, 2116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.