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 746, 454, 980 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 454, 980 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 746, 454, 980 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 746, 454, 980 is 2.
HCF(746, 454, 980) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 454, 980 is 2.
Step 1: Since 746 > 454, we apply the division lemma to 746 and 454, to get
746 = 454 x 1 + 292
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 292 and 454, to get
454 = 292 x 1 + 162
Step 3: We consider the new divisor 292 and the new remainder 162, and apply the division lemma to get
292 = 162 x 1 + 130
We consider the new divisor 162 and the new remainder 130,and apply the division lemma to get
162 = 130 x 1 + 32
We consider the new divisor 130 and the new remainder 32,and apply the division lemma to get
130 = 32 x 4 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 454 is 2
Notice that 2 = HCF(32,2) = HCF(130,32) = HCF(162,130) = HCF(292,162) = HCF(454,292) = HCF(746,454) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 980 > 2, we apply the division lemma to 980 and 2, to get
980 = 2 x 490 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 980 is 2
Notice that 2 = HCF(980,2) .
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 746, 454, 980?
Answer: HCF of 746, 454, 980 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 454, 980 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 454, 980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.