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 552, 698, 845 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 552, 698, 845 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 552, 698, 845 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 552, 698, 845 is 1.
HCF(552, 698, 845) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 552, 698, 845 is 1.
Step 1: Since 698 > 552, we apply the division lemma to 698 and 552, to get
698 = 552 x 1 + 146
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 146 and 552, to get
552 = 146 x 3 + 114
Step 3: We consider the new divisor 146 and the new remainder 114, and apply the division lemma to get
146 = 114 x 1 + 32
We consider the new divisor 114 and the new remainder 32,and apply the division lemma to get
114 = 32 x 3 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 552 and 698 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(114,32) = HCF(146,114) = HCF(552,146) = HCF(698,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 845 > 2, we apply the division lemma to 845 and 2, to get
845 = 2 x 422 + 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 845 is 1
Notice that 1 = HCF(2,1) = HCF(845,2) .
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 552, 698, 845?
Answer: HCF of 552, 698, 845 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 552, 698, 845 using Euclid's Algorithm?
Answer: For arbitrary numbers 552, 698, 845 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.