Highest Common Factor of 690, 3310, 5504 using Euclid's algorithm
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 690, 3310, 5504 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 3310, 5504 is 2 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 690, 3310, 5504 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 690, 3310, 5504 is 2.
HCF(690, 3310, 5504) = 2
HCF of 690, 3310, 5504 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 3310, 5504 is 2.
Highest Common Factor of 690,3310,5504 is 2
Step 1: Since 3310 > 690, we apply the division lemma to 3310 and 690, to get
3310 = 690 x 4 + 550
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 550 and 690, to get
690 = 550 x 1 + 140
Step 3: We consider the new divisor 550 and the new remainder 140, and apply the division lemma to get
550 = 140 x 3 + 130
We consider the new divisor 140 and the new remainder 130,and apply the division lemma to get
140 = 130 x 1 + 10
We consider the new divisor 130 and the new remainder 10,and apply the division lemma to get
130 = 10 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 690 and 3310 is 10
Notice that 10 = HCF(130,10) = HCF(140,130) = HCF(550,140) = HCF(690,550) = HCF(3310,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5504 > 10, we apply the division lemma to 5504 and 10, to get
5504 = 10 x 550 + 4
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get
10 = 4 x 2 + 2
Step 3: 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 10 and 5504 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(5504,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 690, 3310, 5504 using Euclid's Algorithm
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 690, 3310, 5504?
Answer: HCF of 690, 3310, 5504 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 3310, 5504 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 3310, 5504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
