Highest Common Factor of 738, 622, 640 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 738, 622, 640 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 622, 640 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 738, 622, 640 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 738, 622, 640 is 2.
HCF(738, 622, 640) = 2
HCF of 738, 622, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 738, 622, 640 is 2.
Highest Common Factor of 738,622,640 is 2
Step 1: Since 738 > 622, we apply the division lemma to 738 and 622, to get
738 = 622 x 1 + 116
Step 2: Since the reminder 622 ≠ 0, we apply division lemma to 116 and 622, to get
622 = 116 x 5 + 42
Step 3: We consider the new divisor 116 and the new remainder 42, and apply the division lemma to get
116 = 42 x 2 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 738 and 622 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(116,42) = HCF(622,116) = HCF(738,622) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 2, we apply the division lemma to 640 and 2, to get
640 = 2 x 320 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 640 is 2
Notice that 2 = HCF(640,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 738, 622, 640 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 738, 622, 640?
Answer: HCF of 738, 622, 640 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 622, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 622, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.