Highest Common Factor of 390, 936, 744, 712 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 390, 936, 744, 712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 390, 936, 744, 712 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 390, 936, 744, 712 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 390, 936, 744, 712 is 2.
HCF(390, 936, 744, 712) = 2
HCF of 390, 936, 744, 712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 390, 936, 744, 712 is 2.
Highest Common Factor of 390,936,744,712 is 2
Step 1: Since 936 > 390, we apply the division lemma to 936 and 390, to get
936 = 390 x 2 + 156
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 156 and 390, to get
390 = 156 x 2 + 78
Step 3: We consider the new divisor 156 and the new remainder 78, and apply the division lemma to get
156 = 78 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 78, the HCF of 390 and 936 is 78
Notice that 78 = HCF(156,78) = HCF(390,156) = HCF(936,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 744 > 78, we apply the division lemma to 744 and 78, to get
744 = 78 x 9 + 42
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 42 and 78, to get
78 = 42 x 1 + 36
Step 3: We consider the new divisor 42 and the new remainder 36, and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6, and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 78 and 744 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(78,42) = HCF(744,78) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 712 > 6, we apply the division lemma to 712 and 6, to get
712 = 6 x 118 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 712 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(712,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 390, 936, 744, 712 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 390, 936, 744, 712?
Answer: HCF of 390, 936, 744, 712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 390, 936, 744, 712 using Euclid's Algorithm?
Answer: For arbitrary numbers 390, 936, 744, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.