Highest Common Factor of 689, 265, 542, 24 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 689, 265, 542, 24 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 265, 542, 24 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 689, 265, 542, 24 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 689, 265, 542, 24 is 1.
HCF(689, 265, 542, 24) = 1
HCF of 689, 265, 542, 24 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 265, 542, 24 is 1.
Highest Common Factor of 689,265,542,24 is 1
Step 1: Since 689 > 265, we apply the division lemma to 689 and 265, to get
689 = 265 x 2 + 159
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 159 and 265, to get
265 = 159 x 1 + 106
Step 3: We consider the new divisor 159 and the new remainder 106, and apply the division lemma to get
159 = 106 x 1 + 53
We consider the new divisor 106 and the new remainder 53, and apply the division lemma to get
106 = 53 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 53, the HCF of 689 and 265 is 53
Notice that 53 = HCF(106,53) = HCF(159,106) = HCF(265,159) = HCF(689,265) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 542 > 53, we apply the division lemma to 542 and 53, to get
542 = 53 x 10 + 12
Step 2: Since the reminder 53 ≠ 0, we apply division lemma to 12 and 53, to get
53 = 12 x 4 + 5
Step 3: We consider the new divisor 12 and the new remainder 5, and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 53 and 542 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(542,53) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 24 > 1, we apply the division lemma to 24 and 1, to get
24 = 1 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24 is 1
Notice that 1 = HCF(24,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 689, 265, 542, 24 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 689, 265, 542, 24?
Answer: HCF of 689, 265, 542, 24 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 265, 542, 24 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 265, 542, 24 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.