Highest Common Factor of 1640, 7316 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 1640, 7316 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 1640, 7316 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 1640, 7316 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 1640, 7316 is 4.
HCF(1640, 7316) = 4
HCF of 1640, 7316 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1640, 7316 is 4.
Highest Common Factor of 1640,7316 is 4
Step 1: Since 7316 > 1640, we apply the division lemma to 7316 and 1640, to get
7316 = 1640 x 4 + 756
Step 2: Since the reminder 1640 ≠ 0, we apply division lemma to 756 and 1640, to get
1640 = 756 x 2 + 128
Step 3: We consider the new divisor 756 and the new remainder 128, and apply the division lemma to get
756 = 128 x 5 + 116
We consider the new divisor 128 and the new remainder 116,and apply the division lemma to get
128 = 116 x 1 + 12
We consider the new divisor 116 and the new remainder 12,and apply the division lemma to get
116 = 12 x 9 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 1640 and 7316 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(116,12) = HCF(128,116) = HCF(756,128) = HCF(1640,756) = HCF(7316,1640) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1640, 7316 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 1640, 7316?
Answer: HCF of 1640, 7316 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1640, 7316 using Euclid's Algorithm?
Answer: For arbitrary numbers 1640, 7316 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.