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 402, 981, 701 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 981, 701 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 402, 981, 701 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 402, 981, 701 is 1.
HCF(402, 981, 701) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 981, 701 is 1.
Step 1: Since 981 > 402, we apply the division lemma to 981 and 402, to get
981 = 402 x 2 + 177
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 177 and 402, to get
402 = 177 x 2 + 48
Step 3: We consider the new divisor 177 and the new remainder 48, and apply the division lemma to get
177 = 48 x 3 + 33
We consider the new divisor 48 and the new remainder 33,and apply the division lemma to get
48 = 33 x 1 + 15
We consider the new divisor 33 and the new remainder 15,and apply the division lemma to get
33 = 15 x 2 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 402 and 981 is 3
Notice that 3 = HCF(15,3) = HCF(33,15) = HCF(48,33) = HCF(177,48) = HCF(402,177) = HCF(981,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 701 > 3, we apply the division lemma to 701 and 3, to get
701 = 3 x 233 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 701 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(701,3) .
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 402, 981, 701?
Answer: HCF of 402, 981, 701 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 981, 701 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 981, 701 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.