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 712, 451, 975, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 451, 975, 78 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 712, 451, 975, 78 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 712, 451, 975, 78 is 1.
HCF(712, 451, 975, 78) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 451, 975, 78 is 1.
Step 1: Since 712 > 451, we apply the division lemma to 712 and 451, to get
712 = 451 x 1 + 261
Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 261 and 451, to get
451 = 261 x 1 + 190
Step 3: We consider the new divisor 261 and the new remainder 190, and apply the division lemma to get
261 = 190 x 1 + 71
We consider the new divisor 190 and the new remainder 71,and apply the division lemma to get
190 = 71 x 2 + 48
We consider the new divisor 71 and the new remainder 48,and apply the division lemma to get
71 = 48 x 1 + 23
We consider the new divisor 48 and the new remainder 23,and apply the division lemma to get
48 = 23 x 2 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 712 and 451 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(48,23) = HCF(71,48) = HCF(190,71) = HCF(261,190) = HCF(451,261) = HCF(712,451) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 1, we apply the division lemma to 975 and 1, to get
975 = 1 x 975 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 975 is 1
Notice that 1 = HCF(975,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 712, 451, 975, 78?
Answer: HCF of 712, 451, 975, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 451, 975, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 451, 975, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.