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 940, 655, 774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 940, 655, 774 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 940, 655, 774 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 940, 655, 774 is 1.
HCF(940, 655, 774) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 940, 655, 774 is 1.
Step 1: Since 940 > 655, we apply the division lemma to 940 and 655, to get
940 = 655 x 1 + 285
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 285 and 655, to get
655 = 285 x 2 + 85
Step 3: We consider the new divisor 285 and the new remainder 85, and apply the division lemma to get
285 = 85 x 3 + 30
We consider the new divisor 85 and the new remainder 30,and apply the division lemma to get
85 = 30 x 2 + 25
We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 940 and 655 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(85,30) = HCF(285,85) = HCF(655,285) = HCF(940,655) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 5, we apply the division lemma to 774 and 5, to get
774 = 5 x 154 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 774 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(774,5) .
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 940, 655, 774?
Answer: HCF of 940, 655, 774 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 940, 655, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 940, 655, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.