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 678, 7909, 1952 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 7909, 1952 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 678, 7909, 1952 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 678, 7909, 1952 is 1.
HCF(678, 7909, 1952) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 7909, 1952 is 1.
Step 1: Since 7909 > 678, we apply the division lemma to 7909 and 678, to get
7909 = 678 x 11 + 451
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 451 and 678, to get
678 = 451 x 1 + 227
Step 3: We consider the new divisor 451 and the new remainder 227, and apply the division lemma to get
451 = 227 x 1 + 224
We consider the new divisor 227 and the new remainder 224,and apply the division lemma to get
227 = 224 x 1 + 3
We consider the new divisor 224 and the new remainder 3,and apply the division lemma to get
224 = 3 x 74 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 678 and 7909 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(224,3) = HCF(227,224) = HCF(451,227) = HCF(678,451) = HCF(7909,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1952 > 1, we apply the division lemma to 1952 and 1, to get
1952 = 1 x 1952 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1952 is 1
Notice that 1 = HCF(1952,1) .
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 678, 7909, 1952?
Answer: HCF of 678, 7909, 1952 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 7909, 1952 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 7909, 1952 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.