Highest Common Factor of 676, 390, 722 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 676, 390, 722 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 390, 722 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 676, 390, 722 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 676, 390, 722 is 2.
HCF(676, 390, 722) = 2
HCF of 676, 390, 722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 676, 390, 722 is 2.
Highest Common Factor of 676,390,722 is 2
Step 1: Since 676 > 390, we apply the division lemma to 676 and 390, to get
676 = 390 x 1 + 286
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 286 and 390, to get
390 = 286 x 1 + 104
Step 3: We consider the new divisor 286 and the new remainder 104, and apply the division lemma to get
286 = 104 x 2 + 78
We consider the new divisor 104 and the new remainder 78,and apply the division lemma to get
104 = 78 x 1 + 26
We consider the new divisor 78 and the new remainder 26,and apply the division lemma to get
78 = 26 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 676 and 390 is 26
Notice that 26 = HCF(78,26) = HCF(104,78) = HCF(286,104) = HCF(390,286) = HCF(676,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 722 > 26, we apply the division lemma to 722 and 26, to get
722 = 26 x 27 + 20
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 20 and 26, to get
26 = 20 x 1 + 6
Step 3: We consider the new divisor 20 and the new remainder 6, and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 722 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(722,26) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 676, 390, 722 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 676, 390, 722?
Answer: HCF of 676, 390, 722 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 390, 722 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 390, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.