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 454, 740, 672 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 454, 740, 672 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 454, 740, 672 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 454, 740, 672 is 2.
HCF(454, 740, 672) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 454, 740, 672 is 2.
Step 1: Since 740 > 454, we apply the division lemma to 740 and 454, to get
740 = 454 x 1 + 286
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 286 and 454, to get
454 = 286 x 1 + 168
Step 3: We consider the new divisor 286 and the new remainder 168, and apply the division lemma to get
286 = 168 x 1 + 118
We consider the new divisor 168 and the new remainder 118,and apply the division lemma to get
168 = 118 x 1 + 50
We consider the new divisor 118 and the new remainder 50,and apply the division lemma to get
118 = 50 x 2 + 18
We consider the new divisor 50 and the new remainder 18,and apply the division lemma to get
50 = 18 x 2 + 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 454 and 740 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(50,18) = HCF(118,50) = HCF(168,118) = HCF(286,168) = HCF(454,286) = HCF(740,454) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 672 > 2, we apply the division lemma to 672 and 2, to get
672 = 2 x 336 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 672 is 2
Notice that 2 = HCF(672,2) .
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 454, 740, 672?
Answer: HCF of 454, 740, 672 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 454, 740, 672 using Euclid's Algorithm?
Answer: For arbitrary numbers 454, 740, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.