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 774, 986, 525 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 986, 525 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 774, 986, 525 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 774, 986, 525 is 1.
HCF(774, 986, 525) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 986, 525 is 1.
Step 1: Since 986 > 774, we apply the division lemma to 986 and 774, to get
986 = 774 x 1 + 212
Step 2: Since the reminder 774 ≠ 0, we apply division lemma to 212 and 774, to get
774 = 212 x 3 + 138
Step 3: We consider the new divisor 212 and the new remainder 138, and apply the division lemma to get
212 = 138 x 1 + 74
We consider the new divisor 138 and the new remainder 74,and apply the division lemma to get
138 = 74 x 1 + 64
We consider the new divisor 74 and the new remainder 64,and apply the division lemma to get
74 = 64 x 1 + 10
We consider the new divisor 64 and the new remainder 10,and apply the division lemma to get
64 = 10 x 6 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
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 774 and 986 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(64,10) = HCF(74,64) = HCF(138,74) = HCF(212,138) = HCF(774,212) = HCF(986,774) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 525 > 2, we apply the division lemma to 525 and 2, to get
525 = 2 x 262 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 525 is 1
Notice that 1 = HCF(2,1) = HCF(525,2) .
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 774, 986, 525?
Answer: HCF of 774, 986, 525 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 986, 525 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 986, 525 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.