Highest Common Factor of 688, 540 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 688, 540 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 540 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 688, 540 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 688, 540 is 4.
HCF(688, 540) = 4
HCF of 688, 540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 540 is 4.
Highest Common Factor of 688,540 is 4
Step 1: Since 688 > 540, we apply the division lemma to 688 and 540, to get
688 = 540 x 1 + 148
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 148 and 540, to get
540 = 148 x 3 + 96
Step 3: We consider the new divisor 148 and the new remainder 96, and apply the division lemma to get
148 = 96 x 1 + 52
We consider the new divisor 96 and the new remainder 52,and apply the division lemma to get
96 = 52 x 1 + 44
We consider the new divisor 52 and the new remainder 44,and apply the division lemma to get
52 = 44 x 1 + 8
We consider the new divisor 44 and the new remainder 8,and apply the division lemma to get
44 = 8 x 5 + 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 688 and 540 is 4
Notice that 4 = HCF(8,4) = HCF(44,8) = HCF(52,44) = HCF(96,52) = HCF(148,96) = HCF(540,148) = HCF(688,540) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 688, 540 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 688, 540?
Answer: HCF of 688, 540 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.