Highest Common Factor of 280, 392, 770 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 280, 392, 770 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 280, 392, 770 is 14 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 280, 392, 770 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 280, 392, 770 is 14.
HCF(280, 392, 770) = 14
HCF of 280, 392, 770 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 280, 392, 770 is 14.
Highest Common Factor of 280,392,770 is 14
Step 1: Since 392 > 280, we apply the division lemma to 392 and 280, to get
392 = 280 x 1 + 112
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 112 and 280, to get
280 = 112 x 2 + 56
Step 3: We consider the new divisor 112 and the new remainder 56, and apply the division lemma to get
112 = 56 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 280 and 392 is 56
Notice that 56 = HCF(112,56) = HCF(280,112) = HCF(392,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 770 > 56, we apply the division lemma to 770 and 56, to get
770 = 56 x 13 + 42
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 42 and 56, to get
56 = 42 x 1 + 14
Step 3: We consider the new divisor 42 and the new remainder 14, and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 56 and 770 is 14
Notice that 14 = HCF(42,14) = HCF(56,42) = HCF(770,56) .
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Frequently Asked Questions on HCF of 280, 392, 770 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 280, 392, 770?
Answer: HCF of 280, 392, 770 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 280, 392, 770 using Euclid's Algorithm?
Answer: For arbitrary numbers 280, 392, 770 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.