Highest Common Factor of 756, 338, 774, 16 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 756, 338, 774, 16 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 338, 774, 16 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 756, 338, 774, 16 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 756, 338, 774, 16 is 2.
HCF(756, 338, 774, 16) = 2
HCF of 756, 338, 774, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 338, 774, 16 is 2.
Highest Common Factor of 756,338,774,16 is 2
Step 1: Since 756 > 338, we apply the division lemma to 756 and 338, to get
756 = 338 x 2 + 80
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 80 and 338, to get
338 = 80 x 4 + 18
Step 3: We consider the new divisor 80 and the new remainder 18, and apply the division lemma to get
80 = 18 x 4 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 756 and 338 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(80,18) = HCF(338,80) = HCF(756,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 2, we apply the division lemma to 774 and 2, to get
774 = 2 x 387 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 774 is 2
Notice that 2 = HCF(774,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2
Notice that 2 = HCF(16,2) .
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Frequently Asked Questions on HCF of 756, 338, 774, 16 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 756, 338, 774, 16?
Answer: HCF of 756, 338, 774, 16 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 338, 774, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 338, 774, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
