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 697, 360, 524, 700 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 697, 360, 524, 700 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 697, 360, 524, 700 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 697, 360, 524, 700 is 1.
HCF(697, 360, 524, 700) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 697, 360, 524, 700 is 1.
Step 1: Since 697 > 360, we apply the division lemma to 697 and 360, to get
697 = 360 x 1 + 337
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 337 and 360, to get
360 = 337 x 1 + 23
Step 3: We consider the new divisor 337 and the new remainder 23, and apply the division lemma to get
337 = 23 x 14 + 15
We consider the new divisor 23 and the new remainder 15,and apply the division lemma to get
23 = 15 x 1 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 697 and 360 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(337,23) = HCF(360,337) = HCF(697,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 524 > 1, we apply the division lemma to 524 and 1, to get
524 = 1 x 524 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 524 is 1
Notice that 1 = HCF(524,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 700 > 1, we apply the division lemma to 700 and 1, to get
700 = 1 x 700 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 700 is 1
Notice that 1 = HCF(700,1) .
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 697, 360, 524, 700?
Answer: HCF of 697, 360, 524, 700 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 697, 360, 524, 700 using Euclid's Algorithm?
Answer: For arbitrary numbers 697, 360, 524, 700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.