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 7134, 9913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7134, 9913 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 7134, 9913 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 7134, 9913 is 1.
HCF(7134, 9913) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7134, 9913 is 1.
Step 1: Since 9913 > 7134, we apply the division lemma to 9913 and 7134, to get
9913 = 7134 x 1 + 2779
Step 2: Since the reminder 7134 ≠ 0, we apply division lemma to 2779 and 7134, to get
7134 = 2779 x 2 + 1576
Step 3: We consider the new divisor 2779 and the new remainder 1576, and apply the division lemma to get
2779 = 1576 x 1 + 1203
We consider the new divisor 1576 and the new remainder 1203,and apply the division lemma to get
1576 = 1203 x 1 + 373
We consider the new divisor 1203 and the new remainder 373,and apply the division lemma to get
1203 = 373 x 3 + 84
We consider the new divisor 373 and the new remainder 84,and apply the division lemma to get
373 = 84 x 4 + 37
We consider the new divisor 84 and the new remainder 37,and apply the division lemma to get
84 = 37 x 2 + 10
We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get
37 = 10 x 3 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7134 and 9913 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(84,37) = HCF(373,84) = HCF(1203,373) = HCF(1576,1203) = HCF(2779,1576) = HCF(7134,2779) = HCF(9913,7134) .
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 7134, 9913?
Answer: HCF of 7134, 9913 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7134, 9913 using Euclid's Algorithm?
Answer: For arbitrary numbers 7134, 9913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.