Highest Common Factor of 245, 420, 896 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 245, 420, 896 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 245, 420, 896 is 7 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 245, 420, 896 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 245, 420, 896 is 7.
HCF(245, 420, 896) = 7
HCF of 245, 420, 896 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 245, 420, 896 is 7.
Highest Common Factor of 245,420,896 is 7
Step 1: Since 420 > 245, we apply the division lemma to 420 and 245, to get
420 = 245 x 1 + 175
Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 175 and 245, to get
245 = 175 x 1 + 70
Step 3: We consider the new divisor 175 and the new remainder 70, and apply the division lemma to get
175 = 70 x 2 + 35
We consider the new divisor 70 and the new remainder 35, and apply the division lemma to get
70 = 35 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 245 and 420 is 35
Notice that 35 = HCF(70,35) = HCF(175,70) = HCF(245,175) = HCF(420,245) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 896 > 35, we apply the division lemma to 896 and 35, to get
896 = 35 x 25 + 21
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 21 and 35, to get
35 = 21 x 1 + 14
Step 3: We consider the new divisor 21 and the new remainder 14, and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7, and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 35 and 896 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(896,35) .
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Frequently Asked Questions on HCF of 245, 420, 896 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 245, 420, 896?
Answer: HCF of 245, 420, 896 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 245, 420, 896 using Euclid's Algorithm?
Answer: For arbitrary numbers 245, 420, 896 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.