Highest Common Factor of 7164, 1070, 45310 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 7164, 1070, 45310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7164, 1070, 45310 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 7164, 1070, 45310 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 7164, 1070, 45310 is 2.
HCF(7164, 1070, 45310) = 2
HCF of 7164, 1070, 45310 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7164, 1070, 45310 is 2.
Highest Common Factor of 7164,1070,45310 is 2
Step 1: Since 7164 > 1070, we apply the division lemma to 7164 and 1070, to get
7164 = 1070 x 6 + 744
Step 2: Since the reminder 1070 ≠ 0, we apply division lemma to 744 and 1070, to get
1070 = 744 x 1 + 326
Step 3: We consider the new divisor 744 and the new remainder 326, and apply the division lemma to get
744 = 326 x 2 + 92
We consider the new divisor 326 and the new remainder 92,and apply the division lemma to get
326 = 92 x 3 + 50
We consider the new divisor 92 and the new remainder 50,and apply the division lemma to get
92 = 50 x 1 + 42
We consider the new divisor 50 and the new remainder 42,and apply the division lemma to get
50 = 42 x 1 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7164 and 1070 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(50,42) = HCF(92,50) = HCF(326,92) = HCF(744,326) = HCF(1070,744) = HCF(7164,1070) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45310 > 2, we apply the division lemma to 45310 and 2, to get
45310 = 2 x 22655 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 45310 is 2
Notice that 2 = HCF(45310,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7164, 1070, 45310 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 7164, 1070, 45310?
Answer: HCF of 7164, 1070, 45310 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7164, 1070, 45310 using Euclid's Algorithm?
Answer: For arbitrary numbers 7164, 1070, 45310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.