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 553, 657, 772 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 553, 657, 772 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 553, 657, 772 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 553, 657, 772 is 1.
HCF(553, 657, 772) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 553, 657, 772 is 1.
Step 1: Since 657 > 553, we apply the division lemma to 657 and 553, to get
657 = 553 x 1 + 104
Step 2: Since the reminder 553 ≠ 0, we apply division lemma to 104 and 553, to get
553 = 104 x 5 + 33
Step 3: We consider the new divisor 104 and the new remainder 33, and apply the division lemma to get
104 = 33 x 3 + 5
We consider the new divisor 33 and the new remainder 5,and apply the division lemma to get
33 = 5 x 6 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 553 and 657 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(33,5) = HCF(104,33) = HCF(553,104) = HCF(657,553) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 772 > 1, we apply the division lemma to 772 and 1, to get
772 = 1 x 772 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 772 is 1
Notice that 1 = HCF(772,1) .
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 553, 657, 772?
Answer: HCF of 553, 657, 772 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 553, 657, 772 using Euclid's Algorithm?
Answer: For arbitrary numbers 553, 657, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.