Highest Common Factor of 260, 974 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 260, 974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 260, 974 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 260, 974 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 260, 974 is 2.
HCF(260, 974) = 2
HCF of 260, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 260, 974 is 2.
Highest Common Factor of 260,974 is 2
Step 1: Since 974 > 260, we apply the division lemma to 974 and 260, to get
974 = 260 x 3 + 194
Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 194 and 260, to get
260 = 194 x 1 + 66
Step 3: We consider the new divisor 194 and the new remainder 66, and apply the division lemma to get
194 = 66 x 2 + 62
We consider the new divisor 66 and the new remainder 62,and apply the division lemma to get
66 = 62 x 1 + 4
We consider the new divisor 62 and the new remainder 4,and apply the division lemma to get
62 = 4 x 15 + 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 260 and 974 is 2
Notice that 2 = HCF(4,2) = HCF(62,4) = HCF(66,62) = HCF(194,66) = HCF(260,194) = HCF(974,260) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 260, 974 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 260, 974?
Answer: HCF of 260, 974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 260, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 260, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.