Highest Common Factor of 72, 700, 640, 799 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 72, 700, 640, 799 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 700, 640, 799 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 72, 700, 640, 799 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 72, 700, 640, 799 is 1.
HCF(72, 700, 640, 799) = 1
HCF of 72, 700, 640, 799 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 72, 700, 640, 799 is 1.
Highest Common Factor of 72,700,640,799 is 1
Step 1: Since 700 > 72, we apply the division lemma to 700 and 72, to get
700 = 72 x 9 + 52
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 52 and 72, to get
72 = 52 x 1 + 20
Step 3: We consider the new divisor 52 and the new remainder 20, and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 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 72 and 700 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(72,52) = HCF(700,72) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 4, we apply the division lemma to 640 and 4, to get
640 = 4 x 160 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 640 is 4
Notice that 4 = HCF(640,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 799 > 4, we apply the division lemma to 799 and 4, to get
799 = 4 x 199 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: 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 4 and 799 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(799,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 72, 700, 640, 799 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 72, 700, 640, 799?
Answer: HCF of 72, 700, 640, 799 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 700, 640, 799 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 700, 640, 799 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.