Highest Common Factor of 980, 604, 670 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 980, 604, 670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 980, 604, 670 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 980, 604, 670 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 980, 604, 670 is 2.
HCF(980, 604, 670) = 2
HCF of 980, 604, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 980, 604, 670 is 2.
Highest Common Factor of 980,604,670 is 2
Step 1: Since 980 > 604, we apply the division lemma to 980 and 604, to get
980 = 604 x 1 + 376
Step 2: Since the reminder 604 ≠ 0, we apply division lemma to 376 and 604, to get
604 = 376 x 1 + 228
Step 3: We consider the new divisor 376 and the new remainder 228, and apply the division lemma to get
376 = 228 x 1 + 148
We consider the new divisor 228 and the new remainder 148,and apply the division lemma to get
228 = 148 x 1 + 80
We consider the new divisor 148 and the new remainder 80,and apply the division lemma to get
148 = 80 x 1 + 68
We consider the new divisor 80 and the new remainder 68,and apply the division lemma to get
80 = 68 x 1 + 12
We consider the new divisor 68 and the new remainder 12,and apply the division lemma to get
68 = 12 x 5 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 980 and 604 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(68,12) = HCF(80,68) = HCF(148,80) = HCF(228,148) = HCF(376,228) = HCF(604,376) = HCF(980,604) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 670 > 4, we apply the division lemma to 670 and 4, to get
670 = 4 x 167 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 670 is 2
Notice that 2 = HCF(4,2) = HCF(670,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 980, 604, 670 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 980, 604, 670?
Answer: HCF of 980, 604, 670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 980, 604, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 980, 604, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.